Clearwater Paper (CLW) 10-Q 2011 Q3 Quarterly report

Exhibit (32)

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

I, Gordon L. Jones, Chairman and Chief Executive Officer of Clearwater Paper Corporation (the “Company”), certify, pursuant to 18 U.S.C. Section1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:

(1) the Quarterly Report of the Company on Form 10-Q for the period ended September 30, 2011, as filed with the Securities and Exchange Commission on the date hereof (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 condition and results of operations of the Company.

/s/    GORDON L. JONES        

Gordon L. Jones

Chairman and Chief Executive Officer

November 4, 2011

A signed original of this written statement required by Section 906 has been provided to the Company and will be retained by the Company and furnished to the Securities and Exchange Commission or its staff upon request.

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

I, Linda K. Massman, President, Chief Operating Officer and Chief Financial Officer of Clearwater Paper Corporation (the “Company”), certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:

(1) the Quarterly Report of the Company on Form 10-Q for the period ended September 30, 2011, as filed with the Securities and Exchange Commission on the date hereof (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 condition and results of operations of the Company.

/s/    LINDA K. MASSMAN        

Linda K. Massman

President, Chief Operating Officer and Chief Financial Officer

November 4, 2011

A signed original of this written statement required by Section 906 has been provided to the Company and will be retained by the Company and furnished to the Securities and Exchange Commission or its staff upon request.