EXHIBIT 32(b)

                           SECTION 1350 CERTIFICATION

                    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 Annual Report on Form 10-K of The Sherwin-Williams
Company (the "Company") for the fiscal year ended December 31, 2004 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 results of operations of
      the Company.

Dated: March 10, 2005                  /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, or other
document authenticating, acknowledging, or otherwise adopting the signature that
appears in typed form within the electronic version 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.