CERTIFICATE OF AMENDMENT
                                       OF
                          CERTIFICATE OF INCORPORATION
                                       OF
                          TESORO PETROLEUM CORPORATION


     The undersigned, Tesoro Petroleum  Corporation, a Delaware corporation (the
"Corporation"), for the purpose of amending the Certificate of Incorporation  of
the  Corporation, in accordance with the General Corporation Law of the State of
Delaware,  does  hereby  make  and  execute  this  Certificate  of  Amendment of
Certificate of Incorporation and does hereby certify that:

     FIRST:    The following resolution proposed by the Board of  Directors  and
adopted by the stockholders of the Corporation set forth the amendment adopted:

RESOLVED,  that  to  effect  the  Common  Stock Increase, the Board of Directors
          hereby approves and authorizes an  amendment to the first paragraph of
          Article IV and subsection (A) of Article IV of the  Company's  Amended
          and   Restated   Certificate   of  Incorporation  (the  "Common  Stock
          Amendment") by deleting all of  the present first paragraph of Article
          IV and subsection (A) of Article IV and inserting in lieu thereof  the
          following  first paragraph of Article IV and subsection (A) of Article
          IV:

                                  "ARTICLE IV

               The total number of  shares  of  all  classes  of stock which the
          Corporation shall have authority to issue is One Hundred Five  Million
          (105,000,000) shares consisting of

               One Hundred Million (100,000,000) shares of the par value
               $.16 2/3 per share; and

               Five Million (5,000,000) shares with no par value.

          (A)  Designation of Each Class of Shares.

               (1)  The One Hundred Million (100,000,000) authorized
               shares of a par value of $.16 2/3 shall be designated Common
               Stock; and

               (2)  The Five Million (5,000,000) authorized shares with no
               par value shall be designated Preferred Stock."



     SECOND:    Such  amendments  were  duly  adopted  in  accordance  with  the
provisions of Section  242  of  the  General  Corporation  Law  of  the State of
Delaware, as amended.

     IN WITNESS WHEREOF, this Certificate of  Amendment  has  been  executed  on
behalf  of  the Corporation by its Executive Vice President, General Counsel and
Secretary on this 3rd day of August 1998.

                                           TESORO PETROLEUM CORPORATION



                                           By:      /s/ James C. Reed, Jr.

                                                     James C. Reed, Jr.
                                                  Executive Vice President,
                                                General Counsel and Secretary