EXHIBIT 32.1

Certification of Chief Executive Officer 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 Snap-on Incorporated (the “Company”) on Form 10-Q for the period ending October 2, 2004, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), Dale F. Elliott as Chief Executive Officer of the Company, hereby certifies, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, to the best of his knowledge, 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/ Dale F. Elliott
Dale F. Elliott
Chief Executive Officer
November 8, 2004

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