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"),
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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
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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  THAN
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     EXERCISE PRICE.  Excepted  from  the  adjustment  for  anti-dilution
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     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,  the  Company and John and Beverly Karns (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
     -----------------
                                       4635  East  18th  Avenue
                                       Denver,  Colorado  80220
                                       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



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


<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:
                                                 -------------------------------