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 United Rentals, Inc. and United Rentals (North America), Inc. (the “Companies”) on Form 10-K for the year ended December 31, 2010 as filed with the Securities and Exchange Commission (the “Report”), I, William B. Plummer, Chief Financial Officer of the Companies, certify, pursuant to 18 U.S.C. section 1350, as adopted pursuant to section 906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:

1. The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended (15 U.S.C. 78m); and

2. the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Companies.

February 1, 2011

/s/    WILLIAM B. PLUMMER

William B. Plummer

Chief Financial Officer