VOID AFTER 5:00 P.M., MOUNTAIN TIME, ON JUNE 3, 2006

                       WARRANTS TO PURCHASE COMMON SHARES

                                U.S. ENERGY CORP.

This is to certify that, for value received, ___________________ (the "Holder"),
is  entitled to purchase, subject to the terms set forth below, from U.S. Energy
Corp.  (the  "Company"  or  "we"), at any time until 5:00 P.M., Mountain Time on
June 3, 2006 (the "Expiration Date"), ________ shares of the common stock of the
Company  (the  "Common  Shares")  at  a  purchase price per share of $4.00.  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."  This  Warrant  is or may be one of a series of warrants
identical  in  form  issued  by  the  Company to purchase an aggregate of Common
Shares and the term "Warrants" as used herein means all such Warrants (including
this Warrant).  The Common Shares, as adjusted from time to time, underlying the
Warrants  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
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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.  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,  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
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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
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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
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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 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
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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.
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          (1)  ADJUSTMENTS  OF  THE  EXERCISE  PRICE.
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               (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
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          THAN EXERCISE PRICE.
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          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, or
          Common  Shares  issued to acquire a subsidiary or its assets, provided
          such  Common  Shares or Convertible Securities are issued at prices or
          with  exercise  terms equal to the Company's then current market price
          on  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 June 3, 2003,
          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
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          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 the Company's 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  the Company's 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
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          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 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
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          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
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          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
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          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
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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)
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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,
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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
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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
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reclassification,  capital  reorganization or other change of outstanding Common
Shares  (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 Shares on the
record  date  for  payment  of  the  shares  of  the  subsidiary.

     (L)  REGISTRATION UNDER THE SECURITIES ACT OF 1933. As more fully described
          ----------------------------------------------
in  that certain Exchange Agreement dated as of the date hereof by and among the
Holder  and  the Company (the "Exchange Agreement"), the Company agrees with the
Holder  that  the Company shall, on behalf of the Holder, (1) under Section 6 of
the  Act  file,  within  thirty  (30)  days  of  the date hereof, a registration
statement  on Form S-3 with (and use its best efforts to cause such registration
statement  to  be  declared effective as promptly as practicable by) the SEC, to
permit offers and sales involving a public offering (as such term is interpreted
by  the  SEC) under Section 5 of the Act by the Subscriber of the Common Shares;
provided,  however,  that  if  Form  S-3 is not available at that time, then the
Company  shall  file  a registration statement on such form is then available to
effect  a  registration  of  the  Common  Shares,  subject to the consent of the
Holder,  which  consent  will not be unreasonably withheld; and (2) qualify such
offers  and sales of the Common Shares under the securities laws of the state of
residence  of  the  Holder.  The Company shall maintain the effectiveness of the
registration  statement  and  the  current  and  complete  status of the related
prospectus,  at  its  sole  expense,  until  all  Common  Shares have been sold.

     (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
     -----------------
                               1544  York  Street,  Suite  110
                               Denver,  Colorado  80206
                               Attn:  Stephen  E.  Rounds,  Esq.
                               Fax:  303-377-0231

     If  to  the  Holder:
     --------------------





          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.

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

Dated:  June  3,  2003.
                                       U.S.  ENERGY  CORP.


                                       By:
                                           -------------------------------------
                                       Name:
                                            ------------------------------------
                                       Title:
                                             -----------------------------------


                                       -----------------------------------------
                                       Holder


<PAGE>


                                  PURCHASE FORM
     Dated:
The  undersigned hereby irrevocably elects to exercise the Warrant to the extent
of purchasing                    shares of the Company's 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 the Company's 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:
                                                                     -----------