Arch Capital (ACGL) 10-Q 2004 Q3 Quarterly report

Exhibit 32.2

Certification Pursuant to Chapter 63, Title 18 United States Code §1350
As Adopted by Section 906 of the Sarbanes-Oxley Act of 2002
Accompanying Quarterly Report on Form 10-Q of
Arch Capital Group Ltd. for the Fiscal Quarter Ended September 30, 2004

I, John D. Vollaro, Executive Vice President, Chief Financial Officer and Treasurer of Arch Capital Group Ltd. (the “Company”), certify that the accompanying Quarterly Report on Form 10-Q of the Company for the fiscal quarter ended September 30, 2004 fully complies with the requirements of section 13(a) of the Securities Exchange Act of 1934 and the information contained in such report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: November 9, 2004

/s/ John D. Vollaro

John D. Vollaro

Executive Vice President,
Chief Financial Officer and Treasurer

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 Arch Capital Group Ltd. and will be retained by Arch Capital Group Ltd. and furnished to the Securities and Exchange Commission or its staff upon request.