EXHIBIT 32.1

                            CERTIFICATION PURSUANT TO
                             18 U.S.C. SECTION 1350,
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002


In connection with the Annual Report of Tesoro Petroleum Corporation (the
"Company") on Form 10-K for the year ended December 31, 2003 as filed with the
Securities and Exchange Commission on the date hereof (the "Report"), I, Bruce
A. Smith, Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C.
Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of
2002, that:

         (1)      The Report fully complies with the requirements of section
                  13(a) or 15 (d) of the Securities Exchange Act of 1934; and

         (2)      The information contained in the Report fairly presents, in
                  all material respects, the financial condition and results of
                  operations of the Company.



/s/ BRUCE A. SMITH
- -----------------------
Bruce A. Smith
Chief Executive Officer
March 11, 2004


A signed original of this written statement required by Section 906 has been
provided to the Company and will be retained by the Company and furnished to the
Securities and Exchange Commission or its staff upon request.