Filed Pursuant to Rule 424(b)(2)

Registration File No. 333-121626

PROSPECTUS SUPPLEMENT

(To Prospectus dated March 10, 2005 and Prospectus Supplement dated March 14, 2005)

758,367 Shares

Common Stock

Pursuant to an equity distribution agreement with UBS Securities LLC, dated March 14, 2005, during the three months ended March 31, 2005, we sold 758,367 shares of our common stock, par value $0.01 per share, through UBS Securities LLC as our sales agent. The net proceeds to us of the sales of the shares were $41,819,641.18. We paid UBS Securities LLC aggregate commissions of $853,490.72 with respect to the sale of the shares sold through it as agent under the equity distribution agreement.

This prospectus supplement should be read in conjunction with, and may not be delivered or utilized without, the prospectus dated March 10, 2005, and the prospectus supplement dated March 14, 2005.

Our common stock is traded on the New York Stock Exchange under the symbol “FLR.” On May 4, 2005, the last quoted price of the shares of common stock as reported on the NYSE was $53.04.

Investing in these securities involves risks that are described in the “Company Risk Factors” section beginning on page 9 of our Annual Report on Form 10-K for the year ended December 31, 2004, as amended.

Neither the Securities and Exchange Commission nor any state securities commission has approved or disapproved of these securities or determined if this prospectus is truthful or complete. Any representation to the contrary is a criminal offense.

UBS Investment Bank

The date of this prospectus supplement is May 5, 2005