Exhibit 99.1

ARCH CAPITAL GROUP LTD. ANNOUNCES PLAN FOR DEBT OFFERING

HAMILTON, BERMUDA, April 27, 2004 — Arch Capital Group Ltd. [NASDAQ: ACGL] announced today that it plans to commence the marketing for a public offering of $300,000,000 principal amount of its senior notes.  The Company expects to use the net proceeds from the sale of the notes principally to repay all amounts outstanding under its existing credit facility, to support the underwriting activities of its wholly owned insurance and reinsurance subsidiaries and for other general corporate purposes.  The offering will be led by Goldman, Sachs & Co. and JPMorgan.  Credit Suisse First Boston, Merrill Lynch & Co., Banc of America Securities LLC and Wachovia Securities will be co-managers for the offering.

Arch Capital Group Ltd., a Bermuda-based company with approximately $2.1 billion in capital, provides insurance and reinsurance on a worldwide basis through its wholly owned subsidiaries.

This press release shall not constitute an offer to sell or the solicitation of an offer to buy, nor shall there be any sale of these securities in any state in which the offer, solicitation, or sale would be unlawful prior to the registration or qualification under the securities laws of any such state.

A shelf registration statement relating to the securities that the Company plans to sell has previously been filed with, and declared effective by the Securities and Exchange Commission.  Any offer, if at all, will be made only by means of a prospectus, including a prospectus supplement, forming a part of the effective registration statement.

When available, copies of the prospectus relating to this offering may be obtained from Goldman, Sachs & Co., Prospectus Department, 85 Broad Street, New York, NY 10004, telephone: 212-902-1171 and JPMorgan, High Grade Syndicate Desk, 270 Park Avenue, New York, NY 10017, telephone: 212-834-4533.

Cautionary Note Regarding Forward-Looking Statements

The Private Securities Litigation Reform Act of 1995 provides a “safe harbor” for forward-looking statements. This release or any other written or oral statements made

by or on behalf of Arch Capital Group Ltd. and its subsidiaries (collectively, the “Company”) may include forward-looking statements which reflect the Company’s current views with respect to future events and financial performance. Forward-looking statements involve the Company’s current assessment of risks and uncertainties, which may cause actual events and results and prospects to differ materially from those expressed or implied in these statements. Certain information regarding such risks and uncertainties is set forth in the Company’s filings with the Securities and Exchange Commission. The Company undertakes no obligation to publicly update or revise any forward-looking statement, whether as a result of new information, future events or otherwise.

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Contact:	Arch Capital Group Ltd.
	John D. Vollaro
	(441) 278-9250