EXHIBIT 32(b)

CERTIFICATION OF CHIEF FINANCIAL OFFICER

OF

VULCAN MATERIALS COMPANY

PURSUANT TO 18 U.S.C. SECTION 1350

AS ADOPTED PURSUANT TO SECTION 906 OF THE SARBANES OXLEY ACT OF 2002

I, Daniel F. Sansone, Executive Vice President and Chief Financial Officer of Vulcan Materials Company, certify that the Quarterly Report on Form 10-Q (the “report”) for the quarter ended March 31, 2012, filed with the Securities and Exchange Commission on the date hereof:

(i) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended, and

(ii) the information contained in the report fairly presents, in all material respects, the financial condition and results of operations of Vulcan Materials Company.

/s/ Daniel F. Sansone

Daniel F. Sansone, Executive Vice President and Chief Financial Officer

May 2, 2012

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 Vulcan Materials Company and will be retained by Vulcan Materials Company and furnished to the Securities and Exchange Commission or its staff upon request.

Exhibit 32(b)