EXHIBIT 99(b)


                    CERTIFICATION OF CHIEF FINANCIAL 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 on Form 10-Q of The
Sherwin-Williams Company (the "Company") for the period ending September 30,
2002 as filed with the Securities and Exchange Commission on the date hereof
(the "Report"), I, Sean P. Hennessy, Senior Vice President - Finance and Chief
Financial 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:

         (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 result of operations of
         the Company.



Dated:  November 12, 2002             /s/ Sean P. Hennessy
                                      --------------------
                                      Sean P. Hennessy
                                      Senior Vice President - Finance and Chief
                                      Financial Officer