Exhibit 32.1

Certification

of

Chief Executive Officer

Pursuant to 18 U.S.C. 1350

as Adopted Pursuant to

Section 906 of the Sarbanes-Oxley Act of 2002

I, Peter D. Kinnear, Chairman and Chief Executive Officer of FMC Technologies, Inc. (the “Company”), do hereby certify, pursuant to 18 U.S.C. 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(a) the Quarterly Report on Form 10-Q of the Company for the fiscal quarter ended March 31, 2010, as filed with the Securities and Exchange Commission (the “Report”), fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

(b) the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: April 30, 2010