VOID AFTER 5:00 P.M., MOUNTAIN TIME, ON AUGUST 1, 2005

                       WARRANTS TO PURCHASE COMMON SHARES
                                U. S. ENERGY CORP

THIS  IS TO CERTIFY THAT, FOR VALUE RECEIVED, FREDERICK LUTZ, (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
AUGUST  1, 2005 (THE "EXPIRATION DATE") 10,000 SHARES OF THE COMMON STOCK OF THE
COMPANY  (THE  "COMMON  SHARES")  AT  A  PURCHASE PRICE PER SHARE OF $2.00.  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  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
             --------------------
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 THE 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
             ---------------------
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 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.

          (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)     NO ADJUSTMENT FOR SMALL AMOUNTS.  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.

     (H)     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.

     (I)     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.

     (J)     RECLASSIFICATION,  REORGANIZATION  OR  MERGER.  IN  CASE  OF  ANY
             ---------------------------------------------
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 (J) 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
RECORDDATE  FOR  PAYMENT  OF  THE  SHARES  OF  THE  SUBSIDIARY.

     (K)     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:  307-856-9271

     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:              FREDERICK  LUTZ
     -------------------
                                       1089  DUNBARTON  CHASE
                                       ATLANTA,  GEORGIA  30319

     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.

     (L)     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."

     (M)     REGISTRATION  UNDER  THE  SECURITIES  ACT  OF  1933  ("PIGGY  BACK
             ------------------------------------------------------------------
REGISTRATION").  THE  COMPANY  AGREES WITH THE HOLDER THAT THE COMPANY SHALL, ON
-------------
BEHALF  OF THE HOLDER, INCLUDE THE COMMON SHARES FOR PUBLIC RESALE BY THE HOLDER
IN  A  REGISTRATION  STATEMENT  ON  FORM  S-3 TO BE FILED WITH (AND USE ITS BEST
EFFORTS  TO  CAUSE  SUCH  REGISTRATION  STATEMENT  TO  BE  DECLARED EFFECTIVE AS
PROMPTLY  AS  PRACTICABLE  BY)  THE  SEC, SUCH REGISTRATION STATEMENT TO INCLUDE
OTHER SHARES AND SECURITIES FOR RESALE HELD BY OTHER PERSONS. 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)  AS  NECESSARY,  QUALIFY SUCH OFFERS AND SALES OF THE COMMON
SHARES  UNDER  THE SECURITIES LAWS OF THE STATE OF RESIDENCE OF THE HOLDER.  THE
COMPANY  EXPECTS  SUCH  REGISTRATION STATEMENT WILL BE FILED WITH THE SEC IN THE
THIRD  QUARTER  2003.  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.

     (N)     APPLICABLE  LAW.  THIS  WARRANT SHALL BE GOVERNED BY, AND CONSTRUED
             ---------------
IN  ACCORDANCE  WITH,  THE  LAWS  OF  THE  STATE  OF  WYOMING.  IN  THE EVENT OF
LITIGATION,  THE  HOLDER  AGREES  THAT  VENUE  SHALL  BE  IN THE WYOMING COURTS.

                            [EXECUTION PAGE FOLLOWS]

<PAGE>
          IN WITNESS WHEREOF, THE COMPANY AND HOLDER HAVE CAUSED THIS WARRANT TO
BE  EXECUTED  BY  ITS  OFFICER  THEREUNTO  DULY  AUTHORIZED.
DATED:  JULY      2003
             ----

                                       U.  S.  ENERGY  CORP.


                                       BY:
                                          --------------------------------------
                                       NAME:  KEITH  G.  LARSEN
                                       TITLE:  PRESIDENT


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