Exhibit 32

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

Pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, each of the undersigned officers of Dominion Resources, Inc. (the Company), certify that:

1. the Annual Report on Form 10-K for the year ended December 31, 2003 (the “Report”) of the Company to which this certification is an exhibit fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934 (15 U.S.C. 78m(a) or 78o(d)).

2. the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company as of December 31, 2003 and for the period then ended.

/s/    Thos E. Capps        

Thos. E. Capps

President and Chief Executive Officer

March 1, 2004

/s/    Thomas N. Chewning        

Thomas N. Chewning

Executive Vice President and

Chief Financial Officer

March 1, 2004

A signed original of this written statement required by Section 906, or other document authenticating, acknowledging, or otherwise adopting the signature that appears in typed form within the electronic version of this written statement required by Section 906, has been provided to Dominion Resources, Inc. and will be retained by Dominion Resources, Inc. and furnished to the Securities and Exchange Commission or its staff upon request.