Document:

EXHIBIT 4.32

                    CLASS A WARRANT TO PURCHASE COMMON SHARES

                                U.S. ENERGY CORP.

This is to certify that, for value received, Bourne Capital, LLC (the "Holder"),
is entitled to purchase, subject to the terms set forth below, from U.S. Energy
Corp., a Wyoming corporation (the "Company" or "we"), at any time until 5:00
P.M., Mountain Time, on March 2, 2007 (the "Expiration Date," subject to earlier
termination as provided in paragraph (a)) 50,000 shares (the "Common Shares") of
the Company's common stock (the "Common Stock") at a purchase price per share of
$3.00. The number of Common Shares to be received upon the exercise of this
Warrant and the price to be paid for a Common Share may be adjusted from time to
time as hereinafter set forth. The purchase price of a Common Share in effect at
any time and as adjusted from time to time is hereinafter sometimes referred to
as the "Exercise Price." The Common Shares, as adjusted from time to time,
underlying the Warrant are hereinafter sometimes referred to as "Warrant Shares"
and include all Common Shares that have been issued upon the exercise of the
Warrants and all unissued Common Shares underlying the Warrants.

(A) EXERCISE OF WARRANT. This Warrant may be exercised in whole or in part at
any time or from time to time until the Expiration Date or if the Expiration
Date is a day on which banking institutions are authorized by law to close, then
on the next succeeding day which shall not be such a day, by presentation and
surrender hereof to the Company or at the office of its stock transfer agent, if
any, with the Purchase Form annexed hereto duly executed and accompanied by cash
payment of the Exercise Price for the number of shares specified in such Form,
together with all federal and state taxes applicable upon such exercise;
provided, however, that if the closing stock market price for the Company's
Common Stock is at or more than $7.50 for any 10 consecutive trading days, this
Warrant shall expire on the 30th calendar day (or if that day is a Saturday or a
day when banks in New York, New York are closed or authorized to be closed, then
the next business day) after such 10th trading day. The Company shall be under
no obligation to inform the Holder of the Company's stock market price at any
time.

The Company agrees not to merge, reorganize or take any action that would
terminate this Warrant unless provisions are made as part of such merger,
reorganization or other action which would provide the Holder with an equivalent
of this Warrant as specified in Section (i) hereof; provided, however, that if
reasonably required by the other party or parties to such merger, reorganization
or other action, the Company may accelerate the Expiration Date to a date prior
to such merger, reorganization or other action, provided further, however, that
the Company shall give the Holder written notice of such acceleration at least
30 days prior to such accelerated Expiration Date. The Company agrees to provide
notice to the Holder that any tender offer is being made for Common Shares no
later than three business days after the day the Company becomes aware that any
tender offer is being made for outstanding Common Shares. If this Warrant should
be exercised in part only, the Company shall, upon surrender of this Warrant for
cancellation, execute and deliver a new Warrant evidencing the right of the
Holder to purchase the balance of the Common Shares purchasable hereunder. Upon
receipt by the Company of this Warrant at the office of the Company or at the
office of the Company's stock transfer agent, in proper form for exercise and
accompanied by the Exercise Price, the Holder shall be deemed to be

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the holder of record of the Common Shares issuable upon such exercise,
notwithstanding that the stock transfer books of the Company shall then be
closed or that certificates representing such Common Shares shall not then be
actually delivered to the Holder.

(B) RESERVATION OF SHARES. The Company hereby agrees that at all times there
shall be reserved for issuance and/or delivery upon exercise of this Warrant
such number of Common Shares as shall be required for issuance or delivery upon
exercise of this Warrant.

(C) FRACTIONAL SHARES. No fractional shares or scrip representing fractional
shares shall be issued upon the exercise of this Warrant. With respect to any
fraction of a Common Share called for upon any exercise hereof, the Company
shall, upon receipt by the Company or the Company's stock transfer agent of the
Exercise Price on such fractional share, pay to the Holder an amount in cash
equal to such fraction multiplied by the current market value of such fractional
share, determined as follows:

(1) If the Common Shares are listed on a national securities exchange, are
admitted to unlisted trading privileges on such an exchange, or are listed for
trading on a trading system of The Nasdaq Stock Market, Inc., then the current
value shall be the last reported sale price of the Common Shares on such an
exchange or system on the last business day prior to the date of exercise of
this Warrant or if no such sale is made on such day, the average of the closing
bid prices for the Common Shares for such day on such exchange or such system
shall be used; or

(2) If the Common Shares are not so listed on such exchange or system or
admitted to unlisted trading privileges, the current value shall be the average
of the last reported bid prices reported by the National Quotation Bureau, Inc.
on the last business day prior to the date of the exercise of this Warrant; or

(3) If the Common Shares are not so listed or admitted to unlisted trading
privileges and if bid and asked prices are not so reported, the current value
shall be an amount, not less than book value, determined in such reasonable
manner as may be prescribed by the board of directors of the Company.

(D) EXCHANGE, ASSIGNMENT OR LOSS OF WARRANT. This Warrant is exchangeable,
without expense, at the option of the Holder, upon presentation and surrender
hereof to the Company or at the office of its stock transfer agent, if any, for
other Warrants of different denominations entitling the Holder thereof to
purchase (under the same terms and conditions as provided by this Warrant) in
the aggregate the same number of Common Shares purchasable hereunder. This
Warrant may not be sold, transferred, assigned, or hypothecated except in
compliance with the Securities Act of 1933. Any such transfer or assignment
shall be made by surrender of this Warrant to the Company or at the office of
its stock transfer agent, if any, with the Assignment Form annexed hereto duly
executed and with funds sufficient to pay any transfer tax; whereupon the
Company shall, without charge, execute and deliver a new Warrant in the name of
the assignee named in such instrument of assignment and this Warrant shall
promptly be canceled. This Warrant may be divided or combined with other
Warrants which carry the same rights upon presentation hereof at the office of
the Company or at the office of its stock transfer agent, if any, together with
a written notice specifying the names and denominations in which new Warrants
are to be issued and signed by the Holder hereof. The term "Warrant" as used
herein includes

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any warrants issued in substitution for or replacement of this Warrant, or into
which this Warrant may be divided or exchanged. Upon receipt by the Company of
evidence satisfactory to it of the loss, theft, destruction or mutilation of
this Warrant, and (in the case of loss, theft or destruction) of reasonably
satisfactory indemnification, and upon surrender and cancellation of this
Warrant, if mutilated, the Company will execute and deliver a new Warrant of
like tenor and date. Subject to such right of indemnification, any such new
Warrant executed and delivered shall constitute an additional contractual
obligation on the part of the Company, whether or not this Warrant so lost,
stolen, destroyed, or mutilated shall be at any time enforceable by anyone.

(E) RIGHTS OF THE HOLDER. The Holder shall not, by virtue hereof, be entitled to
any rights of a shareholder in the Company, either at law or equity, and the
rights of the Holder are limited to those expressed in the Warrant and are not
enforceable against the Company except to the extent set forth herein.

(F) ADJUSTMENT PROVISIONS.

    (1)     ADJUSTMENTS OF THE EXERCISE PRICE.

(A) If the Company subdivides the outstanding Common Shares into a greater
number of Common Shares, the Exercise Price in effect immediately prior to such
subdivision shall be proportionately reduced. Conversely, if the Company
combines its outstanding Common Shares into a lesser number of Common Shares,
the Exercise Price in effect immediately prior to such combination shall be
proportionally increased. In case of a subdivision or combination, the
adjustment of the Exercise Price shall be made as of the effective date of the
applicable event. A distribution on Common Shares, including a distribution of
Convertible Securities (as that term is defined herein), to shareholders of the
Company on a pro rata basis shall be considered a subdivision of Common Shares
for the purposes of this subsection (1)(A), except that the adjustment will be
made as of the record date for such distribution and any such distribution of
Convertible Securities shall be deemed to be a distribution of the Common Shares
underlying such Convertible Securities. As used herein, the term "Convertible
Securities" shall mean options or warrants or rights for the purchase of Common
Shares or for the purchase of any stock or other securities convertible into or
exchangeable for Common Shares.

(B) If the Company shall at any time distribute or cause to be distributed to
its shareholders, on a pro rata basis, cash, assets, or securities of any entity
other than the Company, then the Exercise Price in effect immediately prior to
such distribution shall automatically be reduced by an amount determined by
dividing (x) the amount (if cash) or the value (if assets or securities) of the
holders' of Warrants (as such term is defined in the first paragraph hereof) pro
rata share of such distribution determined assuming that all holders of Warrants
had exercised their Warrants on the day prior to such distribution, by (y) the
number of Common Shares issuable upon the exercise of this Warrant by the Holder
on the day prior to such distribution.

(2) ADJUSTMENTS OF EXERCISE PRICE - ON ISSUE AT LESS THAN EXERCISE PRICE.
Excepted from the adjustment for anti-dilution provisions of this Section (2)
and Section (3) hereof are the Company's issuance of Excluded Common Shares (as
that term is defined herein), and also all Common Shares or Convertible
Securities in the form of stock options to the Company's employees or
non-executive directors at exercise prices not less than the Company's stock

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market price as of the date of grant, or Common Shares issued to acquire a
subsidiary or its assets, provided such Common Shares are issued at prices not
less than the Company's market price as of the date of such issuance.

If the Company should at any time or from time to time hereafter issue or sell
any of its Common Shares (other than Common Shares issued upon the exercise of
Convertible Securities outstanding on March 2, 2004 (provided such Convertible
Securities have not been amended after March 2, 2004), which Common Shares shall
be referred to herein as the "Excluded Common Shares") without consideration or
for a consideration per share less than the Exercise Price in effect immediately
prior to the time of such issue or sale, then forthwith upon such issue or sale,
the Exercise Price shall be automatically adjusted to a price (computed to the
nearest cent) determined by dividing (i) the sum of (x) the number of Common
Shares outstanding immediately prior to such issue or sale multiplied by the
Exercise Price in effect immediately prior to such issue or sale, and (y) the
consideration, if any, received by the Company upon such issue or sale, by (ii)
the total number of Common Shares outstanding immediately after such issue or
sale. For purposes of this Section (2) and Section (3) hereof, the following
provisions (A) and (B) shall also be applicable:

(A) RIGHTS, OPTIONS OR WARRANTS. In case at any time hereafter the Company shall
in any manner grant any right to subscribe for or to purchase, or any option or
warrant for the purchase of Common Shares or for the purchase of any stock or
securities convertible or exchangeable for Common Shares (such convertible or
exchangeable stock or securities being hereinafter referred to as the
"Underlying Convertible Securities") and if the minimum price per share for
which Common Shares are issuable, pursuant to such rights, options, warrants or
upon conversion or exchange of such Underlying Convertible Securities
(determined by dividing (i) the total amount, if any, received or receivable by
the Company as consideration for the granting of such rights, options, or
warrants plus the minimum aggregate amount of additional consideration payable
to the Company upon the exercise of such rights, options, or warrants under the
terms of such rights, options, or warrants at the time of making such
computation, plus, in the case of such Underlying Convertible Securities, the
minimum aggregate amount of additional consideration, if any, payable upon the
conversion or exchange thereof under the terms of such Underlying Convertible
Securities at the time of making such computation, by (ii) the total maximum
number of Common Shares issuable pursuant to such rights, options, or warrants
or upon the conversion or exchange of the total maximum amount of such
Underlying Convertible Securities issuable upon the exercise of such rights,
options, or warrants or Underlying Convertible Securities at the time of making
such computation) shall be less than the Exercise Price in effect immediately
prior to the time of the granting of such rights or options, then the total
maximum number of Common Shares issuable pursuant to such rights, options,
warrants or upon conversion or exchange of the total maximum amount of such
Underlying Convertible Securities issuable upon the exercise of such rights,
options, or warrants under the terms of such rights, options, warrants or
Underlying Convertible Securities at the time of making such computation shall
(as of the date of granting of such rights, options, or warrants) be deemed to
be outstanding and to have been issued for said price per share as so
determined; provided, that no further adjustment of the Exercise Price shall be
made upon the actual issue of Common Shares so deemed to have been issued unless
the price per share received by the Company upon the actual issuance of Common
Shares so deemed to be issued differs from the price per share which was last
used to adjust the Exercise Price or unless by the terms of such rights,
options, or

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warrants or Underlying Convertible Securities the price per share which the
Company will receive upon any such issuance of Common Shares differs from the
price per share which was last used to adjust the Exercise Price, in either of
which events the Exercise Price shall be adjusted upon the occurrence of either
such event to reflect the new price per share of Common Stock; and further
provided, that, upon the expiration of such rights (including rights to convert
or exchange), options or warrants (a) the number of shares of Common Stock
deemed to have been issued and outstanding by reason of the fact that they were
issuable pursuant to such rights, options, or warrants (including rights to
convert or exchange) that were not exercised, shall no longer be deemed to be
issued and outstanding, and (b) the Exercise Price shall forthwith be adjusted
to the price which would have prevailed had all adjustments been made on the
basis of the issue only of the Common Shares actually issued upon the exercise
of such rights, options, or warrants or upon conversion or exchange of such
Underlying Convertible Securities. Such adjustments upon expiration shall have
no effect on Warrants exercised prior to such expirations.

(B) CONVERTIBLE SECURITIES. If the Company shall in any manner issue or sell any
Convertible Securities other than the rights, options, or warrants described in
this Section (2) or Section (3) hereof and if the minimum price per share for
which Common Shares are issuable upon conversion or exchange of such Convertible
Securities (determined by dividing (i) the total amount received or receivable
by the Company as consideration for the issue or sale of such Convertible
Securities, plus the minimum aggregate amount of additional consideration, if
any, payable to the Company upon the conversion or exchange thereof under the
terms of such Convertible Securities at the time of making such computation, by
(ii) the total maximum number of Common Shares issuable upon the conversion or
exchange of all such Convertible Securities under the terms of such Convertible
Securities at the time of making such computation) shall be less than the
Exercise Price in effect immediately prior to the time of such issue or sale,
then the total maximum number of Common Shares issuable upon conversion or
exchange of all such Convertible Securities at the time of making such
computation shall (as of the date of the issue or sale of such Convertible
Securities) be deemed to be outstanding and to have been issued for said price
per share as so determined; provided, that no further adjustment of the Exercise
Price shall be made upon the actual issue of Common Shares so deemed to have
been issued unless the price per share received by the Company upon the actual
issuance of Common Shares so deemed to be issued differs from the price per
share which was last used to adjust the Exercise Price or unless by the terms of
such Convertible Securities the price per share which the Company will receive
upon any such issuance of Common Shares differs from the price per share which
was last used to adjust the Exercise Price, in either of which events the
Exercise Price shall be adjusted upon the occurrence of either such event to
reflect the new price per share of Common Shares; and, further provided that if
any such issue or sale of such Convertible Securities is made upon exercise of
any right to subscribe for or to purchase or any option to purchase any such
Convertible Securities for which an adjustment of the Exercise Price has been or
is to be made pursuant to the provisions of this Section (2) or Section (3)
hereof, then no further adjustment of the Exercise Price shall be made by reason
of such issue or sale unless the price per share received by the Company upon
the conversion or exchange of such Convertible Securities when actually issued
differs form the price per share which was last used to adjust the Exercise
Price or unless by the terms of uch Convertible Securities the price per share
which the Company will receive upon any such issuance of Common Shares upon
conversion or exchange of such Convertible Securities differs from the price per
share which was last used to adjust the Exercise Price, in either of which
events the Exercise Price shall be

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adjusted upon the occurrence of either of such events to reflect the new price
per share of Common Shares; and, further provided, that, upon the termination of
the right to convert or to exchange of any such Convertible Securities, which
were not so converted or exchange, shall no longer be deemed to be issued and
outstanding, and the Exercise Price shall forthwith be adjusted to the price
which would have prevailed had all adjustments been made on the basis of the
issue only of the number of Common Shares actually issued upon conversion or
exchange of such Convertible Securities. Such adjustments upon expiration shall
have no effect on Warrants exercised prior to such expiration.

(3) DETERMINATION OF ISSUE PRICE. In case any Common Shares or Convertible
Securities which shall be issued for cash, the consideration received therefor,
which shall be the gross sales price for such security without deducting
therefrom any commission or other expenses paid or incurred by the Company for
any underwriting of, or otherwise in connection with, the issuance thereof,
shall be deemed to be the amount received by the Company therefor. In case any
Common Shares or Convertible Securities shall be issued for a consideration part
or all of which shall be other than cash, then the board of directors of the
Company shall determine the fair value of such consideration, irrespective of
accounting treatment, and such Common Shares or Convertible Securities shall be
deemed to have been issued for an amount of cash equal to the value so
determined by the board of directors. The reclassification of securities other
than Common Shares into securities including Common Shares shall be deemed to
involve the issuance for a consideration other than cash of such Common Shares
immediately prior to the close of business on the date fixed for the
determination of security holders entitled to receive such Common Shares. In
case any Common Shares or Convertible Securities shall be issued together with
other stock or securities or other assets of the Company for consideration, the
board of directors of the Company shall determine what part of the consideration
so received is to be deemed to be consideration for the issue of such Common
Shares or Convertible Securities.

(4) DETERMINATION OF DATE OF ISSUE. In case the Company shall take a record of
the holders of Common Shares for the purpose of entitling them (i) to receive a
dividend or other distribution payable in Common Shares or in Convertible
Securities or (ii) to subscribe for or purchase Common Shares or Convertible
Securities, then such record date shall be deemed to be the date of the issue or
sale of the Common Shares deemed to have been issued or sold upon the
declaration of such dividend or the making of such other distribution or the
date of the granting of such right of subscription or purchase, as the case may
be.

(5) TREASURY SHARES. For the purpose of this Section (f), Common Shares at any
relevant time owned or held by, or for the account of, the Company shall not be
deemed outstanding.

         (G) OFFICER'S CERTIFICATE. Whenever the Exercise Price shall be
adjusted as required above, the Company shall forthwith file in the custody of
its Secretary or an Assistant Secretary at its principal office, and with its
stock transfer and warrant agent, if any, an officer's certificate showing the
adjusted Exercise Price determined as herein provided and setting forth in
reasonable detail the facts requiring such adjustment. Each such officer's
certificate shall be made available at all reasonable times for inspection by
the Holder and the Company shall, forthwith after each such adjustment, deliver
a copy of such certificate to the Holder.

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         (H) NO ADJUSTMENT FOR SMALL AMOUNTS. Anything in Sections (2) or (3)
hereof to the contrary notwithstanding, the Company shall not be required to
give effect to any adjustment in the Exercise Price unless and until the net
effect of one or more adjustments, determined as above provided, shall have
required a change of the Exercise Price by at least five cents, but when the
cumulative net effect of more than one adjustment so determined shall be to
change the actual Exercise Price by at least five cents, such change in the
Exercise Price shall thereupon be given effect.

         (I) NUMBER OF SHARES ADJUSTED. Upon any adjustment of the Exercise
Price, the Holder of this Warrant shall thereafter (until another such
adjustment) be entitled to purchase, at the new Exercise Price, the number of
Common Shares, calculated to the nearest full share, obtained by multiplying the
number of Common Shares initially issuable upon exercise of this Warrant by the
Exercise, Price specified in the first paragraph hereof and dividing the product
so obtained by the new Exercise Price.

         (J) NOTICES TO HOLDERS. So long as this Warrant shall be outstanding
and unexercised (i) if the Company shall pay any dividend or make/any
distribution upon the Common Shares or (ii) if the Company shall offer to the
holders of Common Shares for subscription or purchase by them any shares of
stock of any class or any other rights or (iii) if any capital reorganization of
the Company, reclassification of the capital stock of the Company, consolidation
or merger of the Company with or into another corporation, sale, lease or
transfer of all or substantially all of the property and assets of the Company
to another corporation, or voluntary or involuntary dissolution, liquidation or
winding up of the Company shall be effected, then, in any such case, the Company
shall cause to be delivered to the Holder, at least 10 days prior to the date
specified in (x) or (y) below, as the case may be, a notice containing a brief
description of the proposed action and stating the date on which (x) a record is
to be taken for the purpose of such dividend, distribution or rights, or (y)
such reclassification, reorganization, consolidation, merger, conveyance, lease,
dissolution, liquidation or winding up is to take place and the date, if any is
to be fixed, as of which the holders of Common Shares of record shall be
entitled to exchange their Common Shares for securities or other property
deliverable upon such reclassification, reorganization, consolidation, merger,
conveyance, dissolution, liquidation or winding up.

         (K) RECLASSIFICATION, REORGANIZATION OR MERGER. In case of any
reclassification, capital reorganization or other change of outstanding Common
Shares of the Company (other than a change in par value, or from par value to no
par value, or from no par value to par value, or as a result of an issuance of
Common Shares by way of dividend or other distribution or of a subdivision or
combination), or in case of any consolidation or merger of the Company with or
into another corporation (other than a merger with a subsidiary in which merger
the Company is the continuing corporation and which does not result in any
reclassification, capital reorganization or other change of outstanding Common
Shares of the class issuable upon exercise of this Warrant) or in case of any
sale or conveyance to another corporation of the property of the Company as an
entirety or substantially as an entirety, the Company shall cause effective
provision to be made so that the Holder shall have the right thereafter, by
exercising this Warrant, to purchase the kind and amount of shares of stock and
other securities and property which the Holder would have received upon such
reclassification, capital reorganization or other change, consolidation, merger,
sale or conveyance had this

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Warrant been exercised prior to the consummation of such transaction. Any such
provision shall include provision for adjustments which shall be as nearly
equivalent as may be practicable to the adjustments provided for in this
Warrant. The foregoing provisions of this Section (k) shall similarly apply to
successive reclassifications, capital reorganizations and changes of Common
Shares and to successive consolidations, mergers, sales or conveyances. In the
event the Company spins off a subsidiary by distributing to the shareholders of
the Company as a dividend or otherwise the stock of the subsidiary, the Company
shall reserve for the life of this Warrant, shares of the subsidiary to be
delivered to the holders of the Warrants upon exercise to the same extent as if
they were owners of record of the Warrant Share on the record date for payment
of the shares of the subsidiary.

         (L) REGISTRATION UNDER THE SECURITIES ACT OF 1933. The Holder is
entitled to the benefits of Section 5 of that certain Subscription Agreement
dated as of the date hereof by and among the parties hereto (the "Subscription
Agreement"), relating to registration of the Common Shares and the Shares (as
that term is defined in the Subscription Agreement). Such Section 5 is
incorporated by reference into this Warrant.

         (M) NOTICES. All notices required to be given to any of the parties
hereunder shall be in writing and shall be deemed to have been sufficiently
given for all purposes when presented personally to such party or sent by
certified or registered mail, return receipt requested, to such party at its
address set forth below:

         If to the Company:         U.S. Energy Corp.
                                    877 North 8th West
                                    Riverton, Wyoming 82501
                                    Attn: Keith Larsen
                                    Fax: 307-857-3050

         With a copy to:            The Law Offices of Stephen E. Rounds
                                    4635 East 18th Avenue
                                    Denver, Colorado 80220
                                    Attn: Stephen E. Rounds, Esq.
                                    Fax: 303-377-0231

         If to the Subscriber:      Bourne Capital, LLC
                                    410 Marion Street
                                    Denver, Colorado 80218
                                    Attn:  Kevin Daly
                                    Fax: 303-722-7707

         With copies to:            Pepper Hamilton LLP
                                    3000 Two Logan Square
                                    18th & Arch Streets
                                    Philadelphia, Pennsylvania 19103
                                    Attn:  Robert A. Friedel, Esq.
                                    Fax: 215-981-4750

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         Such notice shall be deemed to be given when received if delivered
personally or five (5) business days after the date mailed. Any notice mailed
shall be sent by certified or registered mail. Any notice of any change in such
address shall also be given in the manner set forth above. Whenever the giving
of notice is required, the giving of such notice may be waived in writing by the
party entitled to receive such notice.

         (N) TRANSFER TO COMPLY WITH THE SECURITIES ACT OF 1933. The Company may
cause the following legend, or one similar thereto, to be set forth on the
Warrants and on each certificate representing Warrant Shares or any other
security issued or issuable upon exercise of this Warrant not theretofore
distributed to the public or sold to underwriters for distribution to the
public, unless legal counsel for the Company is of the opinion as to any such
certificate that such legend, or one similar thereto, is unnecessary:

"THE SECURITIES REPRESENTED BY THIS INSTRUMENT HAVE NOT BEEN REGISTERED UNDER
THE SECURITIES ACT OF 1933, AS AMENDED (THE "SECURITIES ACT"), OR ANY STATE
SECURITIES LAWS, AND MAY NOT BE SOLD OR TRANSFERRED OR OFFERED FOR SALE OR
TRANSFER UNLESS A REGISTRATION STATEMENT UNDER THE SECURITIES ACT AND OTHER
APPLICABLE SECURITIES LAWS WITH RESPECT TO SUCH SECURITIES IS THEN IN EFFECT, OR
IN AN OPINION OF COUNSEL OF THE REGISTERED OWNER AND ADDRESSED TO THE ISSUER AND
IN FORM AND SUBSTANCE SATISFACTORY TO THE ISSUER, SUCH REGISTRATION UNDER THE
SECURITIES ACT AND OTHER APPLICABLE SECURITIES LAWS IS NOT REQUIRED."

         (O) APPLICABLE LAW. This Warrant shall be governed by, and construed in
accordance with, the laws of the State of Wyoming.

           [The remainder of this page was intentionally left blank.]

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         IN WITNESS WHEREOF, the Company and Holder have caused this Warrant to
be executed by its officer thereunto duly authorized.
Dated:  March 2, 2004

BOURNE CAPITAL, LLC                         U. S. ENERGY CORP.

By:      /s/  Kevin Daly                    By:     /s/  Keith G. Larsen
    -----------------------------------          -------------------------------
         Name: Kevin Daly                            Name: Keith G. Larsen
        Title:  Managing Member                       Title:  President

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         PURCHASE FORM
                                                 Dated: ________________________

The undersigned hereby irrevocably elects to exercise the Warrant to the extent
of purchasing __________________ shares of Common Stock and hereby makes payment
of $___________________ in payment of the actual exercise price thereof.

INSTRUCTIONS FOR REGISTRATION OF STOCK

Name: __________________________________________________________________________
(Please typewrite or print in block letters)

Address: _______________________________________________________________________

Signature: _____________________________________________________________________

ASSIGNMENT FORM

                                                 Dated: ________________________

     FOR VALUE RECEIVED, _______________________________________________________

hereby sells, assigns and transfers unto _______________________________________

________________________________________________________________________________
(Name:  Please typewrite or print in block letters)

Address: _______________________________________________________________________

the right to purchase Common Stock represented by this Warrant to the extent of

_______________ shares as to which such right is exercisable and does hereby
irrevocably constitute and appoint attorney, to transfer the same on the books
of the Company with full power of substitution in the premises.

                                       Signature: ______________________________

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                    CLASS B WARRANT TO PURCHASE COMMON SHARES

                                U.S. ENERGY CORP.

         This is to certify that, for value received, Bourne Capital, LLC (the
"Holder"), is entitled to purchase, subject to the terms set forth below, from
U.S. Energy Corp., a Wyoming corporation (the "Company" or "we"), at any time
until 5:00 P.M., Mountain Time, on March 2, 2009 (the "Expiration Date," subject
to earlier termination as provided in paragraph (a)) 200,000 shares (the "Common
Shares") of the Company's common stock (the "Common Stock") at a purchase price
per share of $3.00. The number of Common Shares to be received upon the exercise
of this Warrant and the price to be paid for a Common Share may be adjusted from
time to time as hereinafter set forth. The purchase price of a Common Share in
effect at any time and as adjusted from time to time is hereinafter sometimes
referred to as the "Exercise Price." The Common Shares, as adjusted from time to
time, underlying the Warrant are hereinafter sometimes referred to as "Warrant
Shares" and include all Common Shares that have been issued upon the exercise of
the Warrants and all unissued Common Shares underlying the Warrants.

         (A) EXERCISE OF WARRANT. This Warrant may be exercised in whole or in
part at any time or from time to time until the Expiration Date or if the
Expiration Date is a day on which banking institutions are authorized by law to
close, then on the next succeeding day which shall not be such a day, by
presentation and surrender hereof to the Company or at the office of its stock
transfer agent, if any, with the Purchase Form annexed hereto duly executed and
accompanied by cash payment of the Exercise Price for the number of shares
specified in such Form, together with all federal and state taxes applicable
upon such exercise; provided, however, that if the closing stock market price
for the Company's Common Stock is at or more than $7.50 for any 10 consecutive
trading days, this Warrant shall expire on the 30th calendar day (or if that day
is a Saturday or a day when banks in New York, New York are closed or authorized
to be closed, then the next business day) after such 10th trading day. The
Company shall be under no obligation to inform the Holder of the Company's stock
market price at any time.

         The Company agrees not to merge, reorganize or take any action that
would terminate this Warrant unless provisions are made as part of such merger,
reorganization or other action which would provide the Holder with an equivalent
of this Warrant as specified in Section (i) hereof; provided, however, that if
reasonably required by the other party or parties to such merger, reorganization
or other action, the Company may accelerate the Expiration Date to a date prior
to such merger, reorganization or other action, provided further, however, that
the Company shall give the Holder written notice of such acceleration at least
30 days prior to such accelerated Expiration Date. The Company agrees to provide
notice to the Holder that any tender offer is being made for Common Shares no
later than three business days after the day the Company becomes aware that any
tender offer is being made for outstanding Common Shares. If this Warrant should
be exercised in part only, the Company shall, upon surrender of this Warrant for
cancellation, execute and deliver a new Warrant evidencing the right of the
Holder to purchase the balance of the Common Shares purchasable hereunder. Upon
receipt by the Company of this Warrant at the office of the Company or at the
office of the Company's stock transfer agent, in proper form for exercise and
accompanied by the Exercise Price, the Holder shall be deemed to be the holder
of record of the Common Shares issuable upon such exercise,

<PAGE>

notwithstanding that the stock transfer books of the Company shall then be
closed or that certificates representing such Common Shares shall not then be
actually delivered to the Holder.

         (B) RESERVATION OF SHARES. The Company hereby agrees that at all times
there shall be reserved for issuance and/or delivery upon exercise of this
Warrant such number of Common Shares as shall be required for issuance or
delivery upon exercise of this Warrant.

         (C) FRACTIONAL SHARES. No fractional shares or scrip representing
fractional shares shall be issued upon the exercise of this Warrant. With
respect to any fraction of a Common Share called for upon any exercise hereof,
the Company shall, upon receipt by the Company or the Company's stock transfer
agent of the Exercise Price on such fractional share, pay to the Holder an
amount in cash equal to such fraction multiplied by the current market value of
such fractional share, determined as follows:

         (1) If the Common Shares are listed on a national securities exchange,
     are admitted to unlisted trading privileges on such an exchange, or are
     listed for trading on a trading system of The Nasdaq Stock Market, Inc.,
     then the current value shall be the last reported sale price of the Common
     Shares on such an exchange or system on the last business day prior to the
     date of exercise of this Warrant or if no such sale is made on such day,
     the average of the closing bid prices for the Common Shares for such day on
     such exchange or such system shall be used; or

         (2) If the Common Shares are not so listed on such exchange or system
     or admitted to unlisted trading privileges, the current value shall be the
     average of the last reported bid prices reported by the National Quotation
     Bureau, Inc. on the last business day prior to the date of the exercise of
     this Warrant; or

         (3) If the Common Shares are not so listed or admitted to unlisted
     trading privileges and if bid and asked prices are not so reported, the
     current value shall be an amount, not less than book value, determined in
     such reasonable manner as may be prescribed by the board of directors of
     the Company.

         (D) EXCHANGE, ASSIGNMENT OR LOSS OF WARRANT. This Warrant is
exchangeable, without expense, at the option of the Holder, upon presentation
and surrender hereof to the Company or at the office of its stock transfer
agent, if any, for other Warrants of different denominations entitling the
Holder thereof to purchase (under the same terms and conditions as provided by
this Warrant) in the aggregate the same number of Common Shares purchasable
hereunder. This Warrant may not be sold, transferred, assigned, or hypothecated
except in compliance with the Securities Act of 1933. Any such transfer or
assignment shall be made by surrender of this Warrant to the Company or at the
office of its stock transfer agent, if any, with the Assignment Form annexed
hereto duly executed and with funds sufficient to pay any transfer tax;
whereupon the Company shall, without charge, execute and deliver a new Warrant
in the name of the assignee named in such instrument of assignment and this
Warrant shall promptly be canceled. This Warrant may be divided or combined with
other Warrants which carry the same rights upon presentation hereof at the
office of the Company or at the office of its stock transfer agent, if any,
together with a written notice specifying the names and denominations in which
new Warrants are to be issued and signed by the Holder hereof. The term
"Warrant" as used herein includes any warrants issued in substitution for or
replacement of this Warrant, or into which this Warrant may be divided or
exchanged. Upon receipt by the

                                      -2-
<PAGE>

Company of evidence satisfactory to it of the loss, theft, destruction or
mutilation of this Warrant, and (in the case of loss, theft or destruction) of
reasonably satisfactory indemnification, and upon surrender and cancellation of
this Warrant, if mutilated, the Company will execute and deliver a new Warrant
of like tenor and date. Subject to such right of indemnification, any such new
Warrant executed and delivered shall constitute an additional contractual
obligation on the part of the Company, whether or not this Warrant so lost,
stolen, destroyed, or mutilated shall be at any time enforceable by anyone.

         (E) RIGHTS OF THE HOLDER. The Holder shall not, by virtue hereof, be
entitled to any rights of a shareholder in the Company, either at law or equity,
and the rights of the Holder are limited to those expressed in the Warrant and
are not enforceable against the Company except to the extent set forth herein.

         (F) ADJUSTMENT PROVISIONS.

             (1) ADJUSTMENTS OF THE EXERCISE PRICE.

         (A) If the Company subdivides the outstanding Common Shares into a
     greater number of Common Shares, the Exercise Price in effect immediately
     prior to such subdivision shall be proportionately reduced. Conversely, if
     the Company combines its outstanding Common Shares into a lesser number of
     Common Shares, the Exercise Price in effect immediately prior to such
     combination shall be proportionally increased. In case of a subdivision or
     combination, the adjustment of the Exercise Price shall be made as of the
     effective date of the applicable event. A distribution on Common Shares,
     including a distribution of Convertible Securities (as that term is defined
     herein), to shareholders of the Company on a pro rata basis shall be
     considered a subdivision of Common Shares for the purposes of this
     subsection (1)(A), except that the adjustment will be made as of the record
     date for such distribution and any such distribution of Convertible
     Securities shall be deemed to be a distribution of the Common Shares
     underlying such Convertible Securities. As used herein, the term
     "Convertible Securities" shall mean options or warrants or rights for the
     purchase of Common Shares or for the purchase of any stock or other
     securities convertible into or exchangeable for Common Shares.

         (B) If the Company shall at any time distribute or cause to be
     distributed to its shareholders, on a pro rata basis, cash, assets, or
     securities of any entity other than the Company, then the Exercise Price in
     effect immediately prior to such distribution shall automatically be
     reduced by an amount determined by dividing (x)_the amount (if cash) or the
     value (if assets or securities) of the holders' of Warrants (as such term
     is defined in the first paragraph hereof) pro rata share of such
     distribution determined assuming that all holders of Warrants had exercised
     their Warrants on the day prior to such distribution, by (y)_the number of
     Common Shares issuable upon the exercise of this Warrant by the Holder on
     the day prior to such distribution.

         (2) ADJUSTMENTS OF EXERCISE PRICE_- ON ISSUE AT LESS THAN EXERCISE
     PRICE. Excepted from the adjustment for anti-dilution provisions of this
     Section (2) and Section (3) hereof are the Company's issuance of Excluded
     Common Shares (as that term is defined herein), and also all Common Shares
     or Convertible Securities in the form of stock options to the Company's
     employees or non-executive directors at exercise prices not less than the
     Company's stock market price as of the date of grant, or Common Shares
     issued to acquire a subsidiary or its assets, provided such Common Shares
     are issued at prices not less than the Company's market price as of the
     date of such issuance.

                                      -3-
<PAGE>

     If the Company should at any time or from time to time hereafter issue or
     sell any of its Common Shares (other than Common Shares issued upon the
     exercise of Convertible Securities outstanding on March 2, 2004 (provided
     such Convertible Securities have not been amended after March 2, 2004),
     which Common Shares shall be referred to herein as the "Excluded Common
     Shares") without consideration or for a consideration per share less than
     the Exercise Price in effect immediately prior to the time of such issue or
     sale, then forthwith upon such issue or sale, the Exercise Price shall be
     automatically adjusted to a price (computed to the nearest cent) determined
     by dividing (i) the sum of (x) the number of Common Shares outstanding
     immediately prior to such issue or sale multiplied by the Exercise Price in
     effect immediately prior to such issue or sale, and (y) the consideration,
     if any, received by the Company upon such issue or sale, by (ii) the total
     number of Common Shares outstanding immediately after such issue or sale.
     For purposes of this Section (2) and Section (3) hereof, the following
     provisions (A) and (B) shall also be applicable:

         (A) RIGHTS, OPTIONS OR WARRANTS. In case at any time hereafter the
     Company shall in any manner grant any right to subscribe for or to
     purchase, or any option or warrant for the purchase of Common Shares or for
     the purchase of any stock or securities convertible or exchangeable for
     Common Shares (such convertible or exchangeable stock or securities being
     hereinafter referred to as the "Underlying Convertible Securities") and if
     the minimum price per share for which Common Shares are issuable, pursuant
     to such rights, options, warrants or upon conversion or exchange of such
     Underlying Convertible Securities (determined by dividing (i)_the total
     amount, if any, received or receivable by the Company as consideration for
     the granting of such rights, options, or warrants plus the minimum
     aggregate amount of additional consideration payable to the Company upon
     the exercise of such rights, options, or warrants under the terms of such
     rights, options, or warrants at the time of making such computation, plus,
     in the case of such Underlying Convertible Securities, the minimum
     aggregate amount of additional consideration, if any, payable upon the
     conversion or exchange thereof under the terms of such Underlying
     Convertible Securities at the time of making such computation, by (ii)_the
     total maximum number of Common Shares issuable pursuant to such rights,
     options, or warrants or upon the conversion or exchange of the total
     maximum amount of such Underlying Convertible Securities issuable upon the
     exercise of such rights, options, or warrants or Underlying Convertible
     Securities at the time of making such computation) shall be less than the
     Exercise Price in effect immediately prior to the time of the granting of
     such rights or options, then the total maximum number of Common Shares
     issuable pursuant to such rights, options, warrants or upon conversion or
     exchange of the total maximum amount of such Underlying Convertible
     Securities issuable upon the exercise of such rights, options, or warrants
     under the terms of such rights, options, warrants or Underlying Convertible
     Securities at the time of making such computation shall (as of the date of
     granting of such rights, options, or warrants) be deemed to be outstanding
     and to have been issued for said price per share as so determined;
     provided, that no further adjustment of the Exercise Price shall be made
     upon the actual issue of Common Shares so deemed to have been issued unless
     the price per share received by the Company upon the actual issuance of
     Common Shares so deemed to be issued differs from the price per share which
     was last used to adjust the Exercise Price or unless by the terms of such
     rights, options, or warrants or Underlying Convertible Securities the price
     per share which the Company will receive upon any such issuance of Common
     Shares differs from the price per share which was last used to adjust the
     Exercise Price, in either of which events the Exercise Price shall be
     adjusted upon the occurrence of either such event to reflect the new price
     per share of Common Stock; and further provided, that, upon the expiration
     of such rights (including rights to convert or exchange), options or
     warrants (a)_the number of shares of Common Stock deemed to have been
     issued and outstanding by reason of the fact that they were issuable
     pursuant to such rights, options, or warrants (including rights to convert
     or exchange) that were not exercised, shall no

                                      -4-
<PAGE>

     longer be deemed to be issued and outstanding, and (b)_the Exercise Price
     shall forthwith be adjusted to the price which would have prevailed had all
     adjustments been made on the basis of the issue only of the Common Shares
     actually issued upon the exercise of such rights, options, or warrants or
     upon conversion or exchange of such Underlying Convertible Securities. Such
     adjustments upon expiration shall have no effect on Warrants exercised
     prior to such expirations.

         (B) CONVERTIBLE SECURITIES. If the Company shall in any manner issue or
     sell any Convertible Securities other than the rights, options, or warrants
     described in this Section (2) or Section (3) hereof and if the minimum
     price per share for which Common Shares are issuable upon conversion or
     exchange of such Convertible Securities (determined by dividing (i)_the
     total amount received or receivable by the Company as consideration for the
     issue or sale of such Convertible Securities, plus the minimum aggregate
     amount of additional consideration, if any, payable to the Company upon the
     conversion or exchange thereof under the terms of such Convertible
     Securities at the time of making such computation, by (ii) the total
     maximum number of Common Shares issuable upon the conversion or exchange of
     all such Convertible Securities under the terms of such Convertible
     Securities at the time of making such computation) shall be less than the
     Exercise Price in effect immediately prior to the time of such issue or
     sale, then the total maximum number of Common Shares issuable upon
     conversion or exchange of all such Convertible Securities at the time of
     making such computation shall (as of the date of the issue or sale of such
     Convertible Securities) be deemed to be outstanding and to have been issued
     for said price per share as so determined; provided, that no further
     adjustment of the Exercise Price shall be made upon the actual issue of
     Common Shares so deemed to have been issued unless the price per share
     received by the Company upon the actual issuance of Common Shares so deemed
     to be issued differs from the price per share which was last used to adjust
     the Exercise Price or unless by the terms of such Convertible Securities
     the price per share which the Company will receive upon any such issuance
     of Common Shares differs from the price per share which was last used to
     adjust the Exercise Price, in either of which events the Exercise Price
     shall be adjusted upon the occurrence of either such event to reflect the
     new price per share of Common Shares; ad, further provided that if any such
     issue or sale of such Convertible Securities is made upon exercise of any
     right to subscribe for or to purchase or any option to purchase any such
     Convertible Securities for which an adjustment of the Exercise Price has
     been or is to be made pursuant to the provisions of this Section (2) or
     Section (3) hereof, then no further adjustment of the Exercise Price shall
     be made by reason of such issue or sale unless the price per share received
     by the Company upon the conversion or exchange of such Convertible
     Securities when actually issued differs form the price per share which was
     last used to adjust the Exercise Price or unless by the terms of such
     Convertible Securities the price per share which the Company will receive
     upon any such issuance of Common Shares upon conversion or exchange of such
     Convertible Securities differs from the price per share which was last used
     to adjust the Exercise Price, in either of which events the Exercise Price
     shall be adjusted upon the occurrence of either of such events to reflect
     the new price per share of Common Shares; and, further provided, that, upon
     the termination of the right to convert or to exchange of any such
     Convertible Securities, which were not so converted or exchange, shall no
     longer be deemed to be issued and outstanding, and the Exercise Price shall
     forthwith be adjusted to the price which would have prevailed had all
     adjustments been made on the basis of the issue only of the number of
     Common Shares actually issued upon conversion or exchange of such
     Convertible Securities. Such adjustments upon expiration shall have no
     effect on Warrants exercised prior to such expiration.

         (3) DETERMINATION OF ISSUE PRICE. In case any Common Shares or
     Convertible Securities which shall be issued for cash, the consideration
     received therefor, which shall be the gross sales price for such security
     without deducting therefrom any commission or other expenses paid or
     incurred by the Company for any underwriting of, or otherwise in connection
     with, the

                                      -5-
<PAGE>

     issuance thereof, shall be deemed to be the amount received by the Company
     therefor. In case any Common Shares or Convertible Securities shall be
     issued for a consideration part or all of which shall be other than cash,
     then the board of directors of the Company shall determine the fair value
     of such consideration, irrespective of accounting treatment, and such
     Common Shares or Convertible Securities shall be deemed to have been issued
     for an amount of cash equal to the value so determined by the board of
     directors. The reclassification of securities other than Common Shares into
     securities including Common Shares shall be deemed to involve the issuance
     for a consideration other than cash of such Common Shares immediately prior
     to the close of business on the date fixed for the determination of
     security holders entitled to receive such Common Shares. In case any Common
     Shares or Convertible Securities shall be issued together with other stock
     or securities or other assets of the Company for consideration, the board
     of directors of the Company shall determine what part of the consideration
     so received is to be deemed to be consideration for the issue of such
     Common Shares or Convertible Securities.

         (4) DETERMINATION OF DATE OF ISSUE. In case the Company shall take a
     record of the holders of Common Shares for the purpose of entitling them
     (i) to receive a dividend or other distribution payable in Common Shares or
     in Convertible Securities or (ii) to subscribe for or purchase Common
     Shares or Convertible Securities, then such record date shall be deemed to
     be the date of the issue or sale of the Common Shares deemed to have been
     issued or sold upon the declaration of such dividend or the making of such
     other distribution or the date of the granting of such right of
     subscription or purchase, as the case may be.

         (5) TREASURY SHARES. For the purpose of this Section (f), Common Shares
     at any relevant time owned or held by, or for the account of, the Company
     shall not be deemed outstanding.

         (G) OFFICER'S CERTIFICATE. Whenever the Exercise Price shall be
adjusted as required above, the Company shall forthwith file in the custody of
its Secretary or an Assistant Secretary at its principal office, and with its
stock transfer and warrant agent, if any, an officer's certificate showing the
adjusted Exercise Price determined as herein provided and setting forth in
reasonable detail the facts requiring such adjustment. Each such officer's
certificate shall be made available at all reasonable times for inspection by
the Holder and the Company shall, forthwith after each such adjustment, deliver
a copy of such certificate to the Holder.

         (H) NO ADJUSTMENT FOR SMALL AMOUNTS. Anything in Sections (2) or (3)
hereof to the contrary notwithstanding, the Company shall not be required to
give effect to any adjustment in the Exercise Price unless and until the net
effect of one or more adjustments, determined as above provided, shall have
required a change of the Exercise Price by at least five cents, but when the
cumulative net effect of more than one adjustment so determined shall be to
change the actual Exercise Price by at least five cents, such change in the
Exercise Price shall thereupon be given effect.

         (I) NUMBER OF SHARES ADJUSTED. Upon any adjustment of the Exercise
Price, the Holder of this Warrant shall thereafter (until another such
adjustment) be entitled to purchase, at the new Exercise Price, the number of
Common Shares, calculated to the nearest full share, obtained by multiplying the
number of Common Shares initially issuable upon exercise of this Warrant by the
Exercise, Price specified in the first paragraph hereof and dividing the product
so obtained by the new Exercise Price.

                                      -6-
<PAGE>

         (J) NOTICES TO HOLDERS. So long as this Warrant shall be outstanding
and unexercised (i) if the Company shall pay any dividend or make/any
distribution upon the Common Shares or (ii) if the Company shall offer to the
holders of Common Shares for subscription or purchase by them any shares of
stock of any class or any other rights or (iii) if any capital reorganization of
the Company, reclassification of the capital stock of the Company, consolidation
or merger of the Company with or into another corporation, sale, lease or
transfer of all or substantially all of the property and assets of the Company
to another corporation, or voluntary or involuntary dissolution, liquidation or
winding up of the Company shall be effected, then, in any such case, the Company
shall cause to be delivered to the Holder, at least 10 days prior to the date
specified in (x) or (y) below, as the case may be, a notice containing a brief
description of the proposed action and stating the date on which (x) a record is
to be taken for the purpose of such dividend, distribution or rights, or (y)
such reclassification, reorganization, consolidation, merger, conveyance, lease,
dissolution, liquidation or winding up is to take place and the date, if any is
to be fixed, as of which the holders of Common Shares of record shall be
entitled to exchange their Common Shares for securities or other property
deliverable upon such reclassification, reorganization, consolidation, merger,
conveyance, dissolution, liquidation or winding up.

         (K) RECLASSIFICATION, REORGANIZATION OR MERGER. In case of any
reclassification, capital reorganization or other change of outstanding Common
Shares of the Company (other than a change in par value, or from par value to no
par value, or from no par value to par value, or as a result of an issuance of
Common Shares by way of dividend or other distribution or of a subdivision or
combination), or in case of any consolidation or merger of the Company with or
into another corporation (other than a merger with a subsidiary in which merger
the Company is the continuing corporation and which does not result in any
reclassification, capital reorganization or other change of outstanding Common
Shares of the class issuable upon exercise of this Warrant) or in case of any
sale or conveyance to another corporation of the property of the Company as an
entirety or substantially as an entirety, the Company shall cause effective
provision to be made so that the Holder shall have the right thereafter, by
exercising this Warrant, to purchase the kind and amount of shares of stock and
other securities and property which the Holder would have received upon such
reclassification, capital reorganization or other change, consolidation, merger,
sale or conveyance had this Warrant been exercised prior to the consummation of
such transaction. Any such provision shall include provision for adjustments
which shall be as nearly equivalent as may be practicable to the adjustments
provided for in this Warrant. The foregoing provisions of this Section (k) shall
similarly apply to successive reclassifications, capital reorganizations and
changes of Common Shares and to successive consolidations, mergers, sales or
conveyances. In the event the Company spins off a subsidiary by distributing to
the shareholders of the Company as a dividend or otherwise the stock of the
subsidiary, the Company shall reserve for the life of this Warrant, shares of
the subsidiary to be delivered to the holders of the Warrants upon exercise to
the same extent as if they were owners of record of the Warrant Share on the
record date for payment of the shares of the subsidiary.

         (L) REGISTRATION UNDER THE SECURITIES ACT OF 1933. The Holder is
entitled to the benefits of Section 5 of that certain Subscription Agreement
dated as of the date hereof by and among the parties hereto (the "Subscription
Agreement"), relating to registration of the Common Shares and the Shares (as

                                      -7-
<PAGE>

that term is defined in the Subscription Agreement). Such Section 5 is
incorporated by reference into this Warrant.

         (M) NOTICES. All notices required to be given to any of the parties
hereunder shall be in writing and shall be deemed to have been sufficiently
given for all purposes when presented personally to such party or sent by
certified or registered mail, return receipt requested, to such party at its
address set forth below:

         If to the Company:         U.S. Energy Corp.
                                    877 North 8th West
                                    Riverton, Wyoming 82501
                                    Attn: Keith Larsen
                                    Fax: 307-857-3050

         With a copy to:            The Law Offices of Stephen E. Rounds
                                    4635 East 18th Avenue
                                    Denver, Colorado 80220
                                    Attn: Stephen E. Rounds, Esq.
                                    Fax: 303-377-0231

         If to the Subscriber:      Bourne Capital, LLC
                                    410 Marion Street
                                    Denver, Colorado 80218
                                    Attn:  Kevin Daly
                                    Fax: 303-722-7707

         With copies to:            Pepper Hamilton LLP
                                    3000 Two Logan Square
                                    18th & Arch Streets
                                    Philadelphia, Pennsylvania 19103
                                    Attn:  Robert A. Friedel, Esq.
                                    Fax: 215-981-4750

         Such notice shall be deemed to be given when received if delivered
personally or five (5) business days after the date mailed. Any notice mailed
shall be sent by certified or registered mail. Any notice of any change in such
address shall also be given in the manner set forth above. Whenever the giving
of notice is required, the giving of such notice may be waived in writing by the
party entitled to receive such notice.

         (N) TRANSFER TO COMPLY WITH THE SECURITIES ACT OF 1933. The Company may
cause the following legend, or one similar thereto, to be set forth on the
Warrants and on each certificate representing Warrant Shares or any other
security issued or issuable upon exercise of this Warrant not theretofore
distributed to the public or sold to underwriters for distribution to the
public, unless legal counsel for the Company is of the opinion as to any such
certificate that such legend, or one similar thereto, is unnecessary:

         "THE SECURITIES REPRESENTED BY THIS INSTRUMENT HAVE NOT BEEN
         REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE
         "SECURITIES ACT"), OR ANY STATE SECURITIES LAWS, AND MAY NOT
         BE SOLD OR TRANSFERRED OR OFFERED FOR SALE OR TRANSFER UNLESS A

                                 -8-
<PAGE>

         REGISTRATION STATEMENT UNDER THE SECURITIES ACT AND OTHER
         APPLICABLE SECURITIES LAWS WITH RESPECT TO SUCH SECURITIES IS
         THEN IN EFFECT, OR IN AN OPINION OF COUNSEL OF THE REGISTERED
         OWNER AND ADDRESSED TO THE ISSUER AND IN FORM AND SUBSTANCE
         SATISFACTORY TO THE ISSUER, SUCH REGISTRATION UNDER THE
         SECURITIES ACT AND OTHER APPLICABLE SECURITIES LAWS IS NOT
         REQUIRED."

         (O) APPLICABLE LAW. This Warrant shall be governed by, and construed in
accordance with, the laws of the State of Wyoming.

           [The remainder of this page was intentionally left blank.]

                                 -9-
<PAGE>

         IN WITNESS WHEREOF, the Company and Holder have caused this Warrant to
be executed by its officer thereunto duly authorized.

Dated:  March 2, 2004

BOURNE CAPITAL, LLC                           U. S. ENERGY CORP.

By:   /s/  Kevin Daly                         By:    /s/  Keith G. Larsen
    -----------------------------------           ------------------------------
      Name: Kevin Daly                              Name: Keith G. Larsen
      Title:  Managing Member                       Title:  President

                                      -10-
<PAGE>

         PURCHASE FORM

                                                 Dated: ________________________

The undersigned hereby irrevocably elects to exercise the Warrant to the extent
of purchasing __________________ shares of Common Stock and hereby makes payment
of $___________________ in payment of the actual exercise price thereof.

INSTRUCTIONS FOR REGISTRATION OF STOCK

Name: __________________________________________________________________________
(Please typewrite or print in block letters)

Address: _______________________________________________________________________

Signature: _____________________________________________________________________

ASSIGNMENT FORM

                                                 Dated: ________________________

     FOR VALUE RECEIVED, _______________________________________________________

hereby sells, assigns and transfers unto _______________________________________

________________________________________________________________________________
(Name:  Please typewrite or print in block letters)

Address: _______________________________________________________________________

the right to purchase Common Stock represented by this Warrant to the extent of

_______________ shares as to which such right is exercisable and does hereby
irrevocably constitute and appoint attorney, to transfer the same on the books
of the Company with full power of substitution in the premises.

                                       Signature: ______________________________

                                      -11-
<PAGE>EXHIBIT 4.33

NEITHER THIS SECURITY NOR THE SECURITIES INTO WHICH THIS SECURITY IS EXERCISABLE
HAVE BEEN REGISTERED WITH THE SECURITIES AND EXCHANGE COMMISSION OR THE
SECURITIES COMMISSION OF ANY STATE IN RELIANCE UPON AN EXEMPTION FROM
REGISTRATION UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE "SECURITIES
ACT"), AND, ACCORDINGLY, MAY NOT BE OFFERED OR SOLD EXCEPT PURSUANT TO AN
EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES ACT OR PURSUANT TO AN
AVAILABLE EXEMPTION FROM, OR IN A TRANSACTION NOT SUBJECT TO, THE REGISTRATION
REQUIREMENTS OF THE SECURITIES ACT AND IN ACCORDANCE WITH APPLICABLE STATE
SECURITIES LAWS AS EVIDENCED BY A LEGAL OPINION OF COUNSEL TO THE TRANSFEROR
REASONABLY ACCEPTABLE TO THE COMPANY TO SUCH EFFECT, THE SUBSTANCE OF WHICH
SHALL BE REASONABLY ACCEPTABLE TO THE COMPANY. THIS SECURITY MAY BE PLEDGED IN
CONNECTION WITH A BONA FIDE MARGIN ACCOUNT WITH A REGISTERED BROKER-DEALER OR
OTHER LOAN WITH A FINANCIAL INSTITUTION THAT IS AN "ACCREDITED INVESTOR" AS
DEFINED IN RULE 501(a) UNDER THE SECURITIES ACT.

                          COMMON STOCK PURCHASE WARRANT

                To Purchase __________ Shares of Common Stock of

                                U.S. ENERGY CORP.

         THIS COMMON STOCK PURCHASE WARRANT (the "Warrant") CERTIFIES that, for
value received, _____________ (the "Holder"), is entitled, upon the terms and
subject to the limitations on exercise and the conditions hereinafter set forth,
from the day beginning three months after the date of the Purchase Agreement
(the "Initial Exercise Date") as to 25% of the Warrant Shares and an additional
25% of the Warrant Shares on each of the six month, nine month and twelve month
anniversary dates of the date of the Purchase Agreement, and on or prior to the
third anniversary of the Initial Exercise Date (the "Termination Date") but not
thereafter, to subscribe for and purchase from U.S. Energy Corp., a Wyoming
corporation (the "Company"), up to ____________ shares (the "Warrant Shares") of
Common Stock, par value $0.01 per share, of the Company (the "Common Stock");
provided that if the Company exercises its right to Call this Warrant pursuant
to Section 13, the Holder shall have the right to immediately exercise this
Warrant for all Warrant Shares. The purchase price of one share of Common Stock
(the "Exercise Price") under this Warrant shall be 90% of the average of the
five VWAPs immediately preceding the date of exercise, but in no event less than
$1.50 per Warrant Share (subject to adjustment for any stock splits, reverse
stock splits and similar capital events after the issuance date of this
Warrant), and subject to further adjustment hereunder. CAPITALIZED TERMS USED
AND NOT OTHERWISE DEFINED HEREIN SHALL HAVE THE MEANINGS SET FORTH IN THAT
CERTAIN SECURITIES PURCHASE AGREEMENT (THE "PURCHASE AGREEMENT"), DATED FEBRUARY
___, 2004, AMONG THE COMPANY, ROCKY MOUNTAIN GAS, INC. AND THE PURCHASERS
SIGNATORY THERETO.

                                       1

<PAGE>

         1.  TITLE TO WARRANT. Prior to the Termination Date and subject to
compliance with applicable laws and Section 7 of this Warrant, this Warrant and
all rights hereunder are transferable, in whole or in part, at the office or
agency of the Company by the Holder in person or by duly authorized attorney,
upon surrender of this Warrant together with the Assignment Form annexed hereto
properly endorsed. The transferee shall sign an investment letter in form and
substance reasonably satisfactory to the Company.

         2. AUTHORIZATION OF SHARES. The Company covenants that all Warrant
Shares which may be issued upon the exercise of the purchase rights represented
by this Warrant will, upon exercise of the purchase rights represented by this
Warrant, be duly authorized, validly issued, fully paid and nonassessable and
free from all taxes, liens and charges in respect of the issue thereof (other
than taxes in respect of any transfer occurring contemporaneously with such
issue).

         3. EXERCISE OF WARRANT.

              (a) Exercise of the purchase rights represented by this Warrant
     may be made at any time or times on or after the Initial Exercise Date (as
     to that number of Warrant Shares for which this Warrant is then
     exercisable) and on or before the Termination Date by delivery to the
     Company of a duly executed facsimile copy of the Notice of Exercise Form
     annexed hereto (or such other office or agency of the Company as it may
     designate by notice in writing to the registered Holder at the address of
     such Holder appearing on the books of the Company); provided, however,
     within 5 Trading Days of the date said Notice of Exercise is delivered to
     the Company, the Holder shall have surrendered this Warrant to the Company
     and the Company shall have received payment of the aggregate Exercise Price
     of the shares thereby purchased by wire transfer or cashier's check drawn
     on a United States bank. Certificates for shares purchased hereunder shall
     be delivered to the Holder within 3 Trading Days from the delivery to the
     Company of the Notice of Exercise Form, surrender of this Warrant and
     payment of the aggregate Exercise Price as set forth above ("Warrant Share
     Delivery Date"). This Warrant shall be deemed to have been exercised on the
     date the Exercise Price is received by the Company. The Warrant Shares
     shall be deemed to have been issued, and Holder or any other person so
     designated to be named therein shall be deemed to have become a holder of
     record of such shares for all purposes, as of the date the Warrant has been
     exercised by payment to the Company of the Exercise Price and all taxes
     required to be paid by the Holder, if any, pursuant to Section 5 prior to
     the issuance of such shares, have been paid. If the Company fails to
     deliver to the Holder a certificate or certificates representing the
     Warrant Shares pursuant to this Section 3(a) by the third Trading Day
     following the Warrant Share Delivery Date, then the Holder will have the
     right to rescind such exercise. In addition to any other rights available
     to the Holder, if the Company fails to deliver to the Holder a certificate
     or certificates representing the Warrant Shares pursuant to an exercise by
     the third Trading Day after the Warrant Share Delivery Date, and if after
     such day the Holder is required by its broker to purchase (in an open
     market transaction or otherwise) shares of Common Stock to deliver in
     satisfaction of a sale by the Holder of the Warrant Shares which the Holder
     anticipated receiving upon such exercise (a "Buy-In"), then the Company
     shall (1) pay in cash to the Holder the amount by which (x) the Holder's
     total purchase price (including brokerage commissions, if any)

                                        2
<PAGE>

     for the shares of Common Stock so purchased exceeds (y) the amount obtained
     by multiplying (A) the number of Warrant Shares that the Company was
     required to deliver to the Holder in connection with the exercise at issue
     times (B) the price at which the sell order giving rise to such purchase
     obligation was executed, and (2) at the option of the Holder, either
     reinstate the portion of the Warrant and equivalent number of Warrant
     Shares for which such exercise was not honored or deliver to the Holder the
     number of shares of Common Stock that would have been issued had the
     Company timely complied with its exercise and delivery obligations
     hereunder. For example, if the Holder purchases Common Stock having a total
     purchase price of $11,000 to cover a Buy-In with respect to an attempted
     exercise of shares of Common Stock with an aggregate sale price giving rise
     to such purchase obligation of $10,000, under clause (1) of the immediately
     preceding sentence the Company shall be required to pay the Holder $1,000.
     The Holder shall provide the Company written notice indicating the amounts
     payable to the Holder in respect of the Buy-In, together with applicable
     confirmations and other evidence reasonably requested by the Company.
     Nothing herein shall limit a Holder's right to pursue any other remedies
     available to it hereunder, at law or in equity including, without
     limitation, a decree of specific performance and/or injunctive relief with
     respect to the Company's failure to timely deliver certificates
     representing shares of Common Stock upon exercise of the Warrant as
     required pursuant to the terms hereof.

               (b) If this Warrant shall have been exercised in part, the
     Company shall, at the time of delivery of the certificate or certificates
     representing Warrant Shares, deliver to Holder a new Warrant evidencing the
     rights of Holder to purchase the unpurchased Warrant Shares called for by
     this Warrant, which new Warrant shall in all other respects be identical
     with this Warrant.

               (c) The Holder shall not have the right to exercise any portion
     of this Warrant, pursuant to Section 3(a) or otherwise, to the extent that
     after giving effect to such issuance after exercise, the Holder (together
     with the Holder's affiliates), as set forth on the applicable Notice of
     Exercise, would beneficially own in excess of 9.99% of the number of shares
     of the Common Stock outstanding immediately after giving effect to such
     issuance. For purposes of the foregoing sentence, the number of shares of
     Common Stock beneficially owned by the Holder and its affiliates shall
     include the number of shares of Common Stock issuable upon exercise of this
     Warrant with respect to which the determination of such sentence is being
     made, but shall exclude the number of shares of Common Stock which would be
     issuable upon (A) exercise of the remaining, nonexercised portion of this
     Warrant beneficially owned by the Holder or any of its affiliates and (B)
     exercise or conversion of the unexercised or nonconverted portion of any
     other securities of the Company (including, without limitation, any other
     Warrants or the Preferred Stock) subject to a limitation on conversion or
     exercise analogous to the limitation contained herein beneficially owned by
     the Holder or any of its affiliates. Except as set forth in the preceding
     sentence, for purposes of this Section 3(c), beneficial ownership shall be
     calculated in accordance with Section 13(d) of the Exchange Act, it being
     acknowledge by Holder that the Company is not representing to Holder that
     such calculation is in compliance with Section 13(d) of the Exchange Act
     and Holder is solely responsible for any schedules required to be filed in
     accordance therewith. To the extent that the limitation contained in this
     Section 3(c) applies, the determination of whether this

                                       3
<PAGE>

     Warrant is exercisable (in relation to other securities owned by the
     Holder) and of which a portion of this Warrant is exercisable shall be in
     the sole discretion of such Holder, and the submission of a Notice of
     Exercise shall be deemed to be such Holder's determination of whether this
     Warrant is exercisable (in relation to other securities owned by such
     Holder) and of which portion of this Warrant is exercisable, in each case
     subject to such aggregate percentage limitation, and the Company shall have
     no obligation to verify or confirm the accuracy of such determination. For
     purposes of this Section 3(c), in determining the number of outstanding
     shares of Common Stock, the Holder may rely on the number of outstanding
     shares of Common Stock as reflected in (x) the Company's most recent Form
     10-Q or Form 10-K, as the case may be, (y) a more recent public
     announcement by the Company or (z) any other notice by the Company or the
     Company's Transfer Agent setting forth the number of shares of Common Stock
     outstanding. Upon the written or oral request of the Holder, the Company
     shall within two Trading Days confirm orally and in writing to the Holder
     the number of shares of Common Stock then outstanding. In any case, the
     number of outstanding shares of Common Stock shall be determined after
     giving effect to the conversion or exercise of securities of the Company,
     including this Warrant, by the Holder or its affiliates since the date as
     of which such number of outstanding shares of Common Stock was reported.
     The foregoing limitation may be waived by the Holder upon not less than 61
     calendar days' prior written notice to the Company.

               (d) If at any time after one year from the date of issuance of
     this Warrant there is no effective Registration Statement registering the
     resale of the Warrant Shares by the Holder, this Warrant may also be
     exercised at such time by means of a "cashless exercise" in which the
     Holder shall be entitled to receive a certificate for the number of Warrant
     Shares equal to the quotient obtained by dividing [(A-B) (X)] by (A),
     where:

          (A)     = the VWAP on the Trading Day immediately preceding the date
                    of such election;

          (B)     = the Exercise Price of this Warrant, as adjusted; and

          (X)     = the number of Warrant Shares issuable upon exercise of this
                    Warrant in accordance with the terms of this Warrant by
                    means of a cash exercise rather than a cashless exercise.

          4. NO FRACTIONAL SHARES OR SCRIP. No fractional shares or scrip
representing fractional shares shall be issued upon the exercise of this
Warrant. As to any fraction of a share which Holder would otherwise be entitled
to purchase upon such exercise, the Company shall pay a cash adjustment in
respect of such final fraction in an amount equal to such fraction multiplied by
the Exercise Price.

          5. CHARGES, TAXES AND EXPENSES. Issuance of certificates for Warrant
Shares shall be made without charge to the Holder for any issue or transfer tax
or other incidental expense in respect of the issuance of such certificate, all
of which taxes and expenses shall be paid by the Company, and such certificates
shall be issued in the name of the Holder or in such name or names as may be
directed by the Holder; PROVIDED, HOWEVER, that in the event

                                       4
<PAGE>

certificates for Warrant Shares are to be issued in a name other than the name
of the Holder, this Warrant when surrendered for exercise shall be accompanied
by the Assignment Form attached hereto duly executed by the Holder; and the
Company may require, as a condition thereto, the payment of a sum sufficient to
reimburse it for any transfer tax incidental thereto.

          6. CLOSING OF BOOKS. The Company will not close its stockholder books
or records in any manner which prevents the timely exercise of this Warrant,
pursuant to the terms hereof.

          7. TRANSFER, DIVISION AND COMBINATION.

               (a) Subject to compliance with any applicable securities laws and
     the conditions set forth in Sections 1 and 7(e) hereof and to the
     provisions of Section 4.1 of the Purchase Agreement, this Warrant and all
     rights hereunder are transferable, in whole or in part, upon surrender of
     this Warrant at the principal office of the Company, together with a
     written assignment of this Warrant substantially in the form attached
     hereto duly executed by the Holder or its agent or attorney and funds
     sufficient to pay any transfer taxes payable upon the making of such
     transfer. Upon such surrender and, if required, such payment, the Company
     shall execute and deliver a new Warrant or Warrants in the name of the
     assignee or assignees and in the denomination or denominations specified in
     such instrument of assignment, and shall issue to the assignor a new
     Warrant evidencing the portion of this Warrant not so assigned, and this
     Warrant shall promptly be cancelled. A Warrant, if properly assigned, may
     be exercised by a new holder for the purchase of Warrant Shares without
     having a new Warrant issued.

               (b) This Warrant may be divided or combined with other Warrants
     upon presentation hereof at the aforesaid office of the Company, together
     with a written notice specifying the names and denominations in which new
     Warrants are to be issued, signed by the Holder or its agent or attorney.
     Subject to compliance with Section 7(a), as to any transfer which may be
     involved in such division or combination, the Company shall execute and
     deliver a new Warrant or Warrants in exchange for the Warrant or Warrants
     to be divided or combined in accordance with such notice.

               (c) The Company shall prepare, issue and deliver at its own
     expense (other than transfer taxes) the new Warrant or Warrants under this
     Section 7.

               (d) The Company agrees to maintain, at its aforesaid office,
     books for the registration and the registration of transfer of the
     Warrants.

               (e) If, at the time of the surrender of this Warrant in
     connection with any transfer of this Warrant, the transfer of this Warrant
     shall not be registered pursuant to an effective registration statement
     under the Securities Act and under applicable state securities or blue sky
     laws, the Company may require, as a condition of allowing such transfer (i)
     that the Holder or transferee of this Warrant, as the case may be, furnish
     to the Company a written opinion of counsel (which opinion shall be in
     form, substance and scope customary for opinions of counsel in comparable
     transactions) to the effect that such transfer may be made without
     registration under the Securities Act and under

                                       5
<PAGE>

     applicable state securities or blue sky laws, (ii) that the holder or
     transferee execute and deliver to the Company an investment letter in form
     and substance acceptable to the Company and (iii) that the transferee be an
     "accredited investor" as defined in Rule 501(a)(1), (a)(2), (a)(3), (a)(7),
     or (a)(8) promulgated under the Securities Act or a qualified institutional
     buyer as defined in Rule 144A(a) under the Securities Act.

          8. NO RIGHTS AS SHAREHOLDER UNTIL EXERCISE. This Warrant does not
entitle the Holder to any voting rights or other rights as a shareholder of the
Company prior to the exercise hereof. Upon the surrender of this Warrant and the
payment of the aggregate Exercise Price (or by means of a cashless exercise),
the Warrant Shares so purchased shall be and be deemed to be issued to such
Holder as the record owner of such shares as of the close of business on the
later of the date of such surrender or payment.

          9. LOSS, THEFT, DESTRUCTION OR MUTILATION OF WARRANT. The Company
covenants that upon receipt by the Company of evidence reasonably satisfactory
to it of the loss, theft, destruction or mutilation of this Warrant or any stock
certificate relating to the Warrant Shares, and in case of loss, theft or
destruction, of indemnity or security reasonably satisfactory to it (which, in
the case of the Warrant, shall not include the posting of any bond), and upon
surrender and cancellation of such Warrant or stock certificate, if mutilated,
the Company will make and deliver a new Warrant or stock certificate of like
tenor and dated as of such cancellation, in lieu of such Warrant or stock
certificate.

          10. SATURDAYS, SUNDAYS, HOLIDAYS, ETC. If the last or appointed day
for the taking of any action or the expiration of any right required or granted
herein shall be a Saturday, Sunday or a legal holiday, then such action may be
taken or such right may be exercised on the next succeeding day not a Saturday,
Sunday or legal holiday.

          11. ADJUSTMENTS OF EXERCISE PRICE AND NUMBER OF WARRANT SHARES.

               (a) STOCK SPLITS, ETC. The number and kind of securities
     purchasable upon the exercise of this Warrant and the Exercise Price shall
     be subject to adjustment from time to time upon the happening of any of the
     following. In case the Company shall (i) pay a dividend in shares of Common
     Stock or make a distribution in shares of Common Stock to holders of its
     outstanding Common Stock, (ii) subdivide its outstanding shares of Common
     Stock into a greater number of shares, (iii) combine its outstanding shares
     of Common Stock into a smaller number of shares of Common Stock, or (iv)
     issue any shares of its capital stock in a reclassification of the Common
     Stock, then the number of Warrant Shares purchasable upon exercise of this
     Warrant immediately prior thereto shall be adjusted so that the Holder
     shall be entitled to receive the kind and number of Warrant Shares or other
     securities of the Company which it would have owned or have been entitled
     to receive had such Warrant been exercised in advance thereof. Upon each
     such adjustment of the kind and number of Warrant Shares or other
     securities of the Company which are purchasable hereunder, the Holder shall
     thereafter be entitled to purchase the number of Warrant Shares or other
     securities resulting from such adjustment at an Exercise Price per Warrant
     Share or other security obtained by multiplying the Exercise Price in
     effect immediately prior to such adjustment by the number of Warrant Shares
     purchasable pursuant hereto immediately prior to such adjustment and
     dividing by the number of

                                       6
<PAGE>

     Warrant Shares or other securities of the Company that are purchasable
     pursuant hereto immediately thereafter. An adjustment made pursuant to this
     paragraph shall become effective immediately after the effective date of
     such event retroactive to the record date, if any, for such event.

               (b) ANTI-DILUTION PROVISIONS. During the Exercise Period, the
     Exercise Price shall be subject to adjustment from time to time as provided
     in this Section 11(b). In the event that any adjustment of the Exercise
     Price as required herein results in a fraction of a cent, such Exercise
     Price shall be rounded up or down to the nearest cent.

                    (i) ADJUSTMENT OF EXERCISE PRICE. If and whenever the
          Company issues or sells, or in accordance with Section 11(b)(ii)
          hereof is deemed to have issued or sold, any shares of Common Stock
          for an effective consideration per share of less than the then
          Exercise Price or for no consideration (such lower price, the "Base
          Share Price" and such issuances collectively, a "Dilutive Issuance"),
          then, (a) from the Initial Exercise Date until the 30th day following
          the Effective Date (if the Registration Statement is unavailable for
          use by the Holder during such period, such period shall be extended
          for such number of unavailable days), the Exercise Price shall be
          reduced to a price equal to the Base Share Price and (b) after 30th
          day following the Effective Date (as extended in clause (a) above),
          the Exercise Price shall be reduced by multiplying the Exercise Price
          by a fraction, the numerator of which is the number of shares of
          Corporation Common Stock Outstanding immediately prior to the Dilutive
          Issuance plus the number of shares of Corporation Common Stock which
          the offering price for such Dilutive Issuance would purchase at the
          Exercise Price, and the denominator of which shall be the sum of the
          number of shares of Corporation Common Stock Outstanding immediately
          prior to the Dilutive Issuance plus the number of shares of
          Corporation Common Stock so issued or issuable in connection with the
          Dilutive Issuance. Such adjustment shall be made whenever shares of
          Common Stock or Common Stock Equivalents are issued. In no event shall
          the Exercise Price be reduced to a price below $1.00 (as adjusted for
          any stock splits, reverse splits and similar capital events after the
          issuance date of this Warrant.

                    (ii) EFFECT ON EXERCISE PRICE OF CERTAIN EVENTS. For
          purposes of determining the adjusted Exercise Price under Section
          11(b) hereof, the following will be applicable:

                         (A) ISSUANCE OF RIGHTS OR OPTIONS. If the Company in
               any manner issues or grants any warrants, rights or options,
               whether or not immediately exercisable, to subscribe for or to
               purchase Capital Shares or Capital Shares Equivalents (such
               warrants, rights and options to purchase Capital Shares or
               Capital Shares Equivalents are hereinafter referred to as
               "Options") and the effective price per share for which Common
               Stock is issuable upon the exercise of such Options is less than
               the Exercise Price ("Below Base Price Options"), then the maximum
               total number of shares of Common Stock issuable upon the exercise
               of all such Below Base Price Options (assuming full exercise,
               conversion or exchange of Capital Shares

                                       7
<PAGE>

               Equivalents, if applicable) will, as of the date of the issuance
               or grant of such Below Base Price Options, be deemed to be
               outstanding and to have been issued and sold by the Company for
               such price per share and the maximum consideration payable to the
               Company upon such exercise (assuming full exercise, conversion or
               exchange of Capital Shares Equivalents, if applicable) will be
               deemed to have been received by the Company. For purposes of the
               preceding sentence, the "effective price per share for which
               Common Stock is issuable upon the exercise of such Below Base
               Price Options" is determined by dividing (i) the total amount, if
               any, received or receivable by the Company as consideration for
               the issuance or granting of all such Below Base Price Options,
               plus the minimum aggregate amount of additional consideration, if
               any, payable to the Company upon the exercise of all such Below
               Base Price Options, plus, in the case of Capital Shares
               Equivalents issuable upon the exercise of such Below Base Price
               Options, the minimum aggregate amount of additional consideration
               payable upon the exercise, conversion or exchange thereof at the
               time such Capital Shares Equivalents first become exercisable,
               convertible or exchangeable, by (ii) the maximum total number of
               shares of Common Stock issuable upon the exercise of all such
               Below Base Price Options (assuming full conversion of Capital
               Shares Equivalents, if applicable). No further adjustment to the
               Exercise Price will be made upon the actual issuance of such
               Common Stock upon the exercise of such Below Base Price Options
               or upon the exercise, conversion or exchange of Capital Shares
               Equivalents issuable upon exercise of such Below Base Price
               Options.

                         (B) ISSUANCE OF CAPITAL SHARES EQUIVALENTS. If the
               Company in any manner issues or sells any Capital Shares
               Equivalents, whether or not immediately convertible (other than
               where the same are issuable upon the exercise of Options) and the
               effective price per share for which Common Stock is issuable upon
               such exercise, conversion or exchange is less than the Exercise
               Price, then the maximum total number of shares of Common Stock
               issuable upon the exercise, conversion or exchange of all such
               Capital Shares Equivalents will, as of the date of the issuance
               of such Capital Shares Equivalents, be deemed to be outstanding
               and to have been issued and sold by the Company for such price
               per share and the maximum consideration payable to the Company
               upon such exercise (assuming full exercise, conversion or
               exchange of Capital Shares Equivalents, if applicable) will be
               deemed to have been received by the Company. For the purposes of
               the preceding sentence, the "effective price per share for which
               Common Stock is issuable upon such exercise, conversion or
               exchange" is determined by dividing (i) the total amount, if any,
               received or receivable by the Company as consideration for the
               issuance or sale of all such Capital Shares Equivalents, plus the
               minimum aggregate amount of additional consideration, if any,
               payable to the Company upon the exercise, conversion or exchange
               thereof at the time

                                       8
<PAGE>

               such Capital Shares Equivalents first become exercisable,
               convertible or exchangeable, by (ii) the maximum total number of
               shares of Common Stock issuable upon the exercise, conversion or
               exchange of all such Capital Shares Equivalents. No further
               adjustment to the Exercise Price will be made upon the actual
               issuance of such Common Stock upon exercise, conversion or
               exchange of such Capital Shares Equivalents.

                         (C) CHANGE IN OPTION PRICE OR CONVERSION RATE. If there
               is a change at any time in (i) the amount of additional
               consideration payable to the Company upon the exercise of any
               Options; (ii) the amount of additional consideration, if any,
               payable to the Company upon the exercise, conversion or exchange
               of any Capital Shares Equivalents; or (iii) the rate at which any
               Capital Shares Equivalents are convertible into or exchangeable
               for Common Stock (in each such case, other than under or by
               reason of provisions designed to protect against dilution), the
               Exercise Price in effect at the time of such change will be
               readjusted to the Exercise Price which would have been in effect
               at such time had such Options or Capital Shares Equivalents still
               outstanding provided for such changed additional consideration or
               changed conversion rate, as the case may be, at the time
               initially granted, issued or sold.

                         (D) CALCULATION OF CONSIDERATION RECEIVED. If any
               Common Stock, Options or Capital Shares Equivalents are issued,
               granted or sold for cash, the consideration received therefor for
               purposes of this Warrant will be the amount received by the
               Company therefor, before deduction of reasonable commissions,
               underwriting discounts or allowances or other reasonable expenses
               paid or incurred by the Company in connection with such issuance,
               grant or sale. In case any Common Stock, Options or Capital
               Shares Equivalents are issued or sold for a consideration part or
               all of which shall be other than cash, the amount of the
               consideration other than cash received by the Company will be the
               fair market value of such consideration, except where such
               consideration consists of securities, in which case the amount of
               consideration received by the Company will be the fair market
               value (closing bid price, if traded on any market) thereof as of
               the date of receipt. In case any Common Stock, Options or Capital
               Shares Equivalents are issued in connection with any merger or
               consolidation in which the Company is the surviving corporation,
               the amount of consideration therefor will be deemed to be the
               fair market value of such portion of the net assets and business
               of the non-surviving corporation as is attributable to such
               Common Stock, Options or Capital Shares Equivalents, as the case
               may be. The fair market value of any consideration other than
               cash or securities will be determined in good faith by an
               investment banker or other appropriate expert of national
               reputation selected by the Company and reasonably acceptable to
               the holder hereof, with the costs of such appraisal to be borne
               by the Company.

                                       9
<PAGE>

                         (E) EXCEPTIONS TO ADJUSTMENT OF EXERCISE PRICE.
               Notwithstanding the foregoing, no adjustment will be made under
               this Section 11(b) in respect of (1) the granting of options to
               employees, officers or directors of the Company pursuant to any
               stock option plan duly adopted by a majority of the non-employee
               members of the Board of Directors of the Company or a majority of
               the members of a committee of non-employee directors established
               for such purpose or (2) upon the exercise of or conversion of any
               Capital Shares Equivalents or Options issued and outstanding on
               the Initial Exercise Date, provided that the securities have not
               been amended since the date of the Purchase Agreement except as a
               result of the Purchase Agreement.

               (iii) MINIMUM ADJUSTMENT OF EXERCISE PRICE. No adjustment of the
          Exercise Price shall be made in an amount of less than 1% of the
          Exercise Price in effect at the time such adjustment is otherwise
          required to be made, but any such lesser adjustment shall be carried
          forward and shall be made at the time and together with the next
          subsequent adjustment which, together with any adjustments so carried
          forward, shall amount to not less than 1% of such Exercise Price.

          12. REORGANIZATION, RECLASSIFICATION, MERGER, CONSOLIDATION OR
DISPOSITION OF ASSETS. In case the Company shall reorganize its capital,
reclassify its capital stock, consolidate or merge with or into another
corporation (where the Company is not the surviving corporation or where there
is a change in or distribution with respect to the Common Stock of the Company),
or sell, transfer or otherwise dispose of its property, assets or business to
another corporation and, pursuant to the terms of such reorganization,
reclassification, merger, consolidation or disposition of assets, shares of
common stock of the successor or acquiring corporation, or any cash, shares of
stock or other securities or property of any nature whatsoever (including
warrants or other subscription or purchase rights) in addition to or in lieu of
common stock of the successor or acquiring corporation ("Other Property"), are
to be received by or distributed to the holders of Common Stock of the Company,
then the Holder shall have the right thereafter to receive, at the option of the
Holder upon exercise of this Warrant, the number of shares of Common Stock of
the successor or acquiring corporation or of the Company, if it is the surviving
corporation, and Other Property receivable upon or as a result of such
reorganization, reclassification, merger, consolidation or disposition of assets
by a Holder of the number of shares of Common Stock for which this Warrant is
exercisable immediately prior to such event. In case of any such reorganization,
reclassification, merger, consolidation or disposition of assets, the successor
or acquiring corporation (if other than the Company) shall expressly assume the
due and punctual observance and performance of each and every covenant and
condition of this Warrant to be performed and observed by the Company and all
the obligations and liabilities hereunder, subject to such modifications as may
be deemed appropriate (as determined in good faith by resolution of the Board of
Directors of the Company) in order to provide for adjustments of Warrant Shares
for which this Warrant is exercisable which shall be as nearly equivalent as
practicable to the adjustments provided for in this Section 12. For purposes of
this Section 12, "common stock of the successor or acquiring corporation" shall
include stock of such

                                       10
<PAGE>

corporation of any class which is not preferred as to dividends or assets over
any other class of stock of such corporation and which is not subject to
redemption and shall also include any evidences of indebtedness, shares of stock
or other securities which are convertible into or exchangeable for any such
stock, either immediately or upon the arrival of a specified date or the
happening of a specified event and any warrants or other rights to subscribe for
or purchase any such stock. The foregoing provisions of this Section 12 shall
similarly apply to successive reorganizations, reclassifications, mergers,
consolidations or disposition of assets.

          13. CALL PROVISION. Subject to the provisions of this Section 13, if
after the Effective Date the volume weighted average price of the Common Stock
as reported by Bloomberg Financial LP ("VWAP") for each of fifteen consecutive
Trading Days (the "Measurement Price", which period shall not have commenced
until after the Effective Date) exceeds $6.00 (subject to adjustment for any
stock splits, reverse stock splits and similar capital events after the issuance
date of this Warrant) (the "Threshold Price"), then the Company may, within ten
Trading Days of such period, call for cancellation of all or any portion of this
Warrant for which a Notice of Exercise has not yet been delivered (such right, a
"Call"); provided, however, that effective upon delivery of such notice of a
Call, the Holder shall have the right to exercise this Warrant for all Warrant
Shares notwithstanding the vesting schedule set forth in the first paragraph of
this Warrant. To exercise this right, the Company must deliver to the Holder an
irrevocable written notice (a "Call Notice"), indicating therein the portion of
unexercised portion of this Warrant to which such notice applies. If the
conditions set forth below for such Call are satisfied from the period from the
date of the Call Notice through and including the Call Date (as defined below),
then any portion of this Warrant subject to such Call Notice for which a Notice
of Exercise shall not have been received from and after the date of the Call
Notice will be cancelled at 6:30 p.m. (New York City time) on the tenth Trading
Day after the date the Call Notice is received by the Holder (such date, the
"Call Date"). Any unexercised portion of this Warrant to which the Call Notice
does not pertain will be unaffected by such Call Notice. In furtherance thereof,
the Company covenants and agrees that it will honor all Notices of Exercise with
respect to Warrant Shares subject to a Call Notice that are tendered from the
time of delivery of the Call Notice through 6:30 p.m. (New York City time) on
the Call Date, including, without limitation, Notices of Exercise which
otherwise could not be delivered by the Holder because the time periods set
forth in the preamble to this Warrant had not otherwise elapsed. For clarity, it
is agreed that this entire Warrant may be exercised by the Holder upon receipt
of a Call Notice. Notwithstanding anything to the contrary set forth in this
Warrant, the Company may not deliver a Call Notice or require the cancellation
of this Warrant (and any Call Notice will be void), unless, from the beginning
of the 15 consecutive Trading Days used to determine whether the Common Stock
has achieved the Threshold Price through the Call Date, (i) the Company shall
have honored in accordance with the terms of this Warrant all Notices of
Exercise delivered by 6:30 p.m. (New York City time) on the Call Date, (ii) the
Registration Statement shall be effective as to all Warrant Shares and the
prospectus thereunder available for use by the Holder for the resale of all such
Warrant Shares and (iii) the Common Stock shall be listed or quoted for trading
on the Principal Market. The Company's right to Call the Warrant shall be
exercised ratably among the Purchasers based on each Purchaser's initial
purchase of Common Stock pursuant to the Purchase Agreement.

          14. NOTICE OF ADJUSTMENT. Whenever the number of Warrant Shares or
number or kind of securities or other property purchasable upon the exercise of
this Warrant or the Exercise

                                       11
<PAGE>

Price is adjusted, as herein provided, the Company shall give notice thereof to
the Holder, which notice shall state the number of Warrant Shares (and other
securities or property) purchasable upon the exercise of this Warrant and the
Exercise Price of such Warrant Shares (and other securities or property) after
such adjustment, setting forth a brief statement of the facts requiring such
adjustment and setting forth the computation by which such adjustment was made.

          15. NOTICE OF CORPORATE ACTION. If at any time:

               (a) the Company shall take a record of the holders of its Common
     Stock for the purpose of entitling them to receive a dividend or other
     distribution, or any right to subscribe for or purchase any evidences of
     its indebtedness, any shares of stock of any class or any other securities
     or property, or to receive any other right, or

               (b) there shall be any capital reorganization of the Company, any
     reclassification or recapitalization of the capital stock of the Company or
     any consolidation or merger of the Company with, or any sale, transfer or
     other disposition of all or substantially all the property, assets or
     business of the Company to, another corporation or,

               (c) there shall be a voluntary or involuntary dissolution,
     liquidation or winding up of the Company;

then, in any one or more of such cases, the Company shall give to Holder (i) at
least 20 days' prior written notice of the date on which a record date shall be
selected for such dividend, distribution or right or for determining rights to
vote in respect of any such reorganization, reclassification, merger,
consolidation, sale, transfer, disposition, liquidation or winding up, and (ii)
in the case of any such reorganization, reclassification, merger, consolidation,
sale, transfer, disposition, dissolution, liquidation or winding up, at least 20
days' prior written notice of the date when the same shall take place. Such
notice in accordance with the foregoing clause also shall specify (i) the date
on which any such record is to be taken for the purpose of such dividend,
distribution or right, the date on which the holders of Common Stock shall be
entitled to any such dividend, distribution or right, and the amount and
character thereof, and (ii) the date on which any such reorganization,
reclassification, merger, consolidation, sale, transfer, disposition,
dissolution, liquidation or winding up is to take place and the time, if any
such time is to be fixed, as of which the holders of Common Stock shall be
entitled to exchange their Warrant Shares for securities or other property
deliverable upon such disposition, dissolution, liquidation or winding up. Each
such written notice shall be sufficiently given if addressed to Holder at the
last address of Holder appearing on the books of the Company and delivered in
accordance with Section 17(d).

          16. AUTHORIZED SHARES. The Company covenants that during the period
the Warrant is outstanding, it will reserve from its authorized and unissued
Common Stock a sufficient number of shares to provide for the issuance of the
Warrant Shares upon the exercise of any purchase rights under this Warrant. The
Company further covenants that its issuance of this Warrant shall constitute
full authority to its officers who are charged with the duty of executing stock
certificates to execute and issue the necessary certificates for the Warrant
Shares upon the exercise of the purchase rights under this Warrant. The Company
will take all such

                                       12
<PAGE>

reasonable action as may be necessary to assure that such Warrant Shares may be
issued as provided herein without violation of any applicable law or regulation,
or of any requirements of the Principal Market upon which the Common Stock may
be listed.

          Except and to the extent as waived or consented to by the Holder, the
Company shall not by any action, including, without limitation, amending its
certificate of incorporation or through any reorganization, transfer of assets,
consolidation, merger, dissolution, issue or sale of securities or any other
voluntary action, avoid or seek to avoid the observance or performance of any of
the terms of this Warrant, but will at all times in good faith assist in the
carrying out of all such terms and in the taking of all such actions as may be
necessary or appropriate to protect the rights of Holder as set forth in this
Warrant against impairment. Without limiting the generality of the foregoing,
the Company will (a) not increase the par value of any Warrant Shares above the
amount payable therefor upon such exercise immediately prior to such increase in
par value, (b) take all such action as may be necessary or appropriate in order
that the Company may validly and legally issue fully paid and nonassessable
Warrant Shares upon the exercise of this Warrant, and (c) use commercially
reasonable efforts to obtain all such authorizations, exemptions or consents
from any public regulatory body having jurisdiction thereof as may be necessary
to enable the Company to perform its obligations under this Warrant.

          Before taking any action which would result in an adjustment in the
number of Warrant Shares for which this Warrant is exercisable or in the
Exercise Price, the Company shall obtain all such authorizations or exemptions
thereof, or consents thereto, as may be necessary from any public regulatory
body or bodies having jurisdiction thereof.

          17. MISCELLANEOUS.

               (a) JURISDICTION. All questions concerning the construction,
     validity, enforcement and interpretation of this Warrant shall be
     determined in accordance with the provisions of the Purchase Agreement.

               (b) RESTRICTIONS. The Holder acknowledges that the Warrant Shares
     acquired upon the exercise of this Warrant, if not registered, will have
     restrictions upon resale imposed by state and federal securities laws.

               (c) NONWAIVER AND EXPENSES. No course of dealing or any delay or
     failure to exercise any right hereunder on the part of Holder shall operate
     as a waiver of such right or otherwise prejudice Holder's rights, powers or
     remedies, notwithstanding all rights hereunder terminate on the Termination
     Date. If the Company willfully and knowingly fails to comply with any
     provision of this Warrant, which results in any material damages to the
     Holder, the Company shall pay to Holder such amounts as shall be sufficient
     to cover any costs and expenses including, but not limited to, reasonable
     attorneys' fees, including those of appellate proceedings, incurred by
     Holder in collecting any amounts due pursuant hereto or in otherwise
     enforcing any of its rights, powers or remedies hereunder.

                                       13
<PAGE>

               (d) NOTICES. Any notice, request or other document required or
     permitted to be given or delivered to the Holder by the Company shall be
     delivered in accordance with the notice provisions of the Purchase
     Agreement.

               (e) LIMITATION OF LIABILITY. No provision hereof, in the absence
     of any affirmative action by Holder to exercise this Warrant or purchase
     Warrant Shares, and no enumeration herein of the rights or privileges of
     Holder, shall give rise to any liability of Holder for the purchase price
     of any Common Stock or as a stockholder of the Company, whether such
     liability is asserted by the Company or by creditors of the Company.

               (f) REMEDIES. Holder, in addition to being entitled to exercise
     all rights granted by law, including recovery of damages, will be entitled
     to specific performance of its rights under this Warrant. The Company
     agrees that monetary damages would not be adequate compensation for any
     loss incurred by reason of a breach by it of the provisions of this Warrant
     and hereby agrees to waive the defense in any action for specific
     performance that a remedy at law would be adequate.

               (g) SUCCESSORS AND ASSIGNS. Subject to applicable securities
     laws, this Warrant and the rights and obligations evidenced hereby shall
     inure to the benefit of and be binding upon the successors of the Company
     and the successors and permitted assigns of Holder. The provisions of this
     Warrant are intended to be for the benefit of all Holders from time to time
     of this Warrant and shall be enforceable by any such Holder or holder of
     Warrant Shares.

               (h) AMENDMENT. This Warrant may be modified or amended or the
     provisions hereof waived with the written consent of the Company and the
     Holder.

               (i) SEVERABILITY. Wherever possible, each provision of this
     Warrant shall be interpreted in such manner as to be effective and valid
     under applicable law, but if any provision of this Warrant shall be
     prohibited by or invalid under applicable law, such provision shall be
     ineffective to the extent of such prohibition or invalidity, without
     invalidating the remainder of such provisions or the remaining provisions
     of this Warrant.

               (j) HEADINGS. The headings used in this Warrant are for the
     convenience of reference only and shall not, for any purpose, be deemed a
     part of this Warrant.

                              ********************

                                       14
<PAGE>

          IN WITNESS WHEREOF, the Company has caused this Warrant to be executed
by its officer thereunto duly authorized.

Dated:  February __, 2004
                                        U.S. Energy Corp.

                                        By:  /s/  Keith G. Larsen
                                            ------------------------------------
                                                 Name:  Keith G. Larsen
                                                 Title: President

                                       15
<PAGE>

                               NOTICE OF EXERCISE

To:  U.S Energy Corp.

          (1) The undersigned hereby elects to purchase ________ Warrant Shares
of the Company pursuant to the terms of the attached Warrant (only if exercised
in full), and tenders herewith payment of the exercise price in full, together
with all applicable transfer taxes, if any.

          (2) Payment shall take the form of (check applicable box):

               [  ] in lawful money of the United States; or

               [  ] the cancellation of such number of Warrant Shares as is
               necessary, in accordance with the formula set forth in subsection
               3(d), to exercise this Warrant with respect to the maximum number
               of Warrant Shares purchasable pursuant to the cashless exercise
               procedure set forth in subsection 3(d).

          (3) Please issue a certificate or certificates representing said
Warrant Shares in the name of the undersigned or in such other name as is
specified below:

               ________________________________________

The Warrant Shares shall be delivered to the following:

               ________________________________________

               ________________________________________

               ________________________________________

          (4) Accredited Investor. The undersigned is an "accredited investor"
as defined in Regulation D under the Securities Act of 1933, as amended.

                                        [PURCHASER]

                                        By: ______________________________
                                        Name:
                                        Title:

                                        Dated:  ________________________

<PAGE>

                                 ASSIGNMENT FORM

                    (To assign the foregoing warrant, execute
                   this form and supply required information.
                 Do not use this form to exercise the warrant.)

          FOR VALUE RECEIVED, the foregoing Warrant and all rights evidenced
thereby are hereby assigned to

_______________________________________________ whose address is

________________________________________________________________.

_________________________________________________________________

                                       Dated:  ______________, _______

              Holder's Signature: _______________________________

              Holder's Address:__________________________________

                               __________________________________

Signature Guaranteed: ___________________________________________

NOTE: The signature to this Assignment Form must correspond with the name as it
appears on the face of the Warrant, without alteration or enlargement or any
change whatsoever, and must be guaranteed by a bank or trust company. Officers
of corporations and those acting in a fiduciary or other representative capacity
should file proper evidence of authority to assign the foregoing Warrant.

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