Exhibit 32.1

CERTIFICATION BY CEO 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 quarterly report of General Dynamics Corporation (the Company) on Form 10-Q for the quarter ended September 28, 2008, as filed with the Securities and Exchange Commission on the date hereof (the Report), I, Nicholas D. Chabraja, Chairman and 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 to my knowledge:

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/ Nicholas D. Chabraja

Nicholas D. Chabraja

Chairman and Chief Executive Officer

November 4, 2008

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.