AMENDMENT TO

                      WARRANT TO PURCHASE 200,000 COMMON SHARES

                                  U.S. ENERGY CORP.


               WHEREAS,  SHAMROCK  PARTNERS,  LTD.   of 111 Veterans Square
          Media,  PA  19063  ("Holder") was granted a warrant  to  purchase
          200,000 common shares  of U.S. Energy Corp. $.01 par value common
          stock on January 9, 1996 (the "Warrant"), with an Expiration Date
          of January 9, 1997.

               NOW  THEREFORE,  U.S.   Energy  Corp.   hereby  extends  the
          Expiration Date of the Warrant to July 9, 1997.


               DATED, nunc pro tunc January 8, 1997.


                                                  U.S. ENERGY CORP.

                                             By:      s/ John L.  Larsen
                                                  --------------------------
                                                  JOHN L. LARSEN, President