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 March 31, 2003 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: May 13, 2003                     /s/ Sean P. Hennessy
                                        ----------------------------------------
                                        Sean P. Hennessy
                                        Senior Vice President - Finance and
                                        Chief Financial Officer


A signed original of this written statement required by Section 906 has been
provided to The Sherwin-Williams Company and will be retained by The
Sherwin-Williams Company and furnished to The Securities and Exchange Commission
or its staff upon request.