Exhibit 32.2

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, John M. Zinzarella, Vice President of Finance, Treasurer and Chief Financial Officer of the Company, 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/ John M. Zinzarella

John M. Zinzarella, CPA

Vice President of Finance, Treasurer and

Chief Financial Officer

March 25, 2004