Exhibit 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350

ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Annual Report of Moore Medical Corp. (the “Company”) on Form 10-K for the period ended December 27, 2003 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Linda M. Autore, President and Chief Executive Officer of the Company and member of the Board of Directors, certify, pursuant to Section 18 U.S.C. 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) and 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/ Linda M. Autore

Linda M. Autore

President and Chief Executive Officer

March 25, 2004