Exhibit 32.01

                            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 Valero Energy Corporation (the Company)
on Form 10-K for the year ending December 31, 2004, as filed with the Securities
and Exchange Commission on the date hereof (the Report), I, William E. Greehey,
Chief Executive Officer of the Company, hereby 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/ William E. Greehey
- -----------------------
William E. Greehey
Chief Executive Officer
March 11, 2005

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



                            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 Valero Energy Corporation (the Company)
on Form 10-K for the year ending December 31, 2004, as filed with the Securities
and Exchange Commission on the date hereof (the Report), I, Michael S.
Ciskowski, Executive Vice President and Chief Financial Officer of the Company,
hereby 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/ Michael S. Ciskowski
- ----------------------------------------------------
Michael S. Ciskowski
Executive Vice President and Chief Financial Officer
March 11, 2005

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