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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<PAGE>


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



                                      -5-
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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



                                      -7-
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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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<PAGE>


         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






                                      -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: ______________________________






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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>