Exhibit 5.1

2 April 2012

Arch Capital Group Ltd.

Wessex House, 5th Floor

45 Reid Street

Hamilton HM 12

Bermuda

Dear Sirs,

Arch Capital Group Ltd. (the “Company”)

We have acted as special legal counsel in Bermuda to the Company in connection with the offer and sale by the Company of 13,000,000 of its 6.75% Non-Cumulative Preferred Shares, Series C (the “Preferred Shares”) as described in the Company’s registration statement on Form S-3 (Registration No. 333-180329) which was declared effective on 23 March 2012 (the “Registration Statement”), filed under the U.S. Securities Act of 1933, as amended, with the U.S. Securities and Exchange Commission, the Company’s prospectus dated 23 March 2012 (the “Base Prospectus”), as supplemented by the prospectus supplement dated 26 March 2012 (the “Prospectus Supplement” and together with the Base Prospectus, the “Prospectus”).

For the purposes of giving this opinion, we have examined electronic copies of the following documents:

(i)             the Registration Statement;

(ii)            the Prospectus;

(iii)          that certain Purchase Agreement dated 26 March 2012 among the Company and Wells Fargo Securities, LLC, Merrill Lynch, Pierce, Fenner & Smith Incorporated,

Morgan Stanley & Co. LLC and UBS Securities LLC as representatives of the several underwriters named in Schedule A thereto;

(iv)                   the Certificate of Designations of the Preferred Shares dated 2 April 2012; and

(v)                      a specimen certificate representing the Preferred Shares (the “Preferred Share Certificate”).

The documents listed in items (i) through (v) above are herein sometimes collectively referred to as the “Documents” (which term does not include any other instrument or agreement whether or not specifically referred to therein or attached as an exhibit or schedule thereto).  We have also reviewed the memorandum of association and the bye-laws of the Company, each certified by the Secretary of the Company on 2 April 2012 (together, the “Constitutional Documents”), extracts of minutes of a meeting of the Company’s Board of Directors held on 29 February 2012, certified by the Secretary of the Company on 23 March 2012 and 30 March 2012 (the resolutions contained in such extracts and minutes being collectively referred to herein as the “Resolutions”), a copy of an officer’s certificate dated 26 March 2012 signed by the Chief Financial Officer of the Company, and such other documents and made such enquiries as to questions of law as we have deemed necessary in order to render the opinion set forth below.

We have assumed (a) the genuineness and authenticity of all signatures and the conformity to the originals of all copies (whether or not certified) examined by us and the authenticity and completeness of the originals from which such copies were taken, (b) that where a document has been examined by us in draft form, it will be or has been executed and/or filed in the form of that draft, and where a number of drafts of a document have been examined by us all changes thereto have been marked or otherwise drawn to our attention, (c) the accuracy and completeness of all factual representations made in the Documents and other documents reviewed by us, (d) that the Resolutions were passed at one or more duly convened, constituted and quorate meetings, or by unanimous written resolutions, remain in full force and effect and have not been rescinded or amended, (e) that there is no provision of the law of any jurisdiction, other than Bermuda, which would have any implication in relation to the opinions expressed herein, (f) that upon the issue of any shares the Company will receive consideration for the full issue price thereof which shall be equal to at least the par value thereof, (g) that on the date of issuance of the Preferred Shares, the Company will be able to pay its liabilities as they become due.

We have made no investigation of and express no opinion in relation to the laws of any jurisdiction other than Bermuda.  This opinion is to be governed by and construed in accordance with the laws of Bermuda and is limited to and is given on the basis of the

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current law and practice in Bermuda.  This opinion is issued solely for your benefit and use in connection with the matter described herein and is not to be relied upon by any other person, firm or entity or in respect of any other matter.

On the basis of and subject to the foregoing, we are of the opinion that:

1.                           The Company is duly incorporated and existing under the laws of Bermuda in good standing (meaning solely that it has not failed to make any required filing with any Bermuda governmental authority, or to pay any Bermuda government fee or tax, which would make it liable to be struck off the Register of Companies and thereby cease to exist under the laws of Bermuda).

2.                           The Preferred Shares have been duly authorised and, when issued and paid for as contemplated by the Prospectus, will be validly issued, fully paid and non-assessable (which term means when used herein that no further sums are required to be paid by the holders thereof in connection with the issue of such shares).

3.                           The form of the Preferred Share Certificate complies with the requirements of Bermuda law and is not inconsistent with any provision of the Constitutional Documents.

We hereby consent to the filing of this opinion as an exhibit to the Company’s Current Report on Form 8-K filed on 2 April 2012 and to the references to our firm under the caption, “Legal Matters” in the Prospectus forming part of the Registration Statement.  In giving this consent, we do not hereby admit that we are experts within the meaning of Section 11 of the Securities Act or that we are in the categories of persons whose consent is required under Section 7 of the Securities Act or the Rules and Regulations of the Commission promulgated thereunder.

Yours faithfully,

Conyers Dill & Pearman Limited

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