Exhibit 32 (b)

CERTIFICATION 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 of West Pharmaceutical Services, Inc. (the “Company”) on Form 10-K for the period ending December 31, 2005 filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, William J. Federici, Vice President 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 position and results of operations of the Company.

/s/ William J. Federici

William J. Federici

Vice President and Chief Financial Officer

March 3, 2006