Ownership Submission
FORM 4
Check this box if no longer subject to Section 16. Form 4 or Form 5 obligations may continue. See Instruction 1(b).
UNITED STATES SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP OF SECURITIES

Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934, Section 17(a) of the Public Utility Holding Company Act of 1935 or Section 30(h) of the Investment Company Act of 1940
OMB APPROVAL
OMB Number: 3235-0287
Expires: January 31, 2005
Estimated average burden hours per response... 0.5

(Print or Type Responses)
1. Name and Address of Reporting Person *
BUNCE JOHN L JR
   2. Issuer Name and Ticker or Trading Symbol
ARCH CAPITAL GROUP LTD. [ACGL] 		5. Relationship of Reporting Person(s) to Issuer
(Check all applicable)
__X__ Director _____ 10% Owner
_____ Officer (give title below) _____ Other (specify below)
(Last)
(First)
(Middle)
HELLMAN & FRIEDMAN LLC, ONE MARITIME PLAZA 12TH FLOOR		 3. Date of Earliest Transaction (Month/Day/Year)
05/03/2006
(Street)

SAN FRANCISCO, CA 94111		 4. If Amendment, Date Original Filed(Month/Day/Year)
 6. Individual or Joint/Group Filing(Check Applicable Line)
_X_ Form filed by One Reporting Person
___ Form filed by More than One Reporting Person
(City)
(State)
(Zip)
Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned
1.Title of Security
(Instr. 3)		 2. Transaction Date (Month/Day/Year) 2A. Deemed Execution Date, if any (Month/Day/Year) 3. Transaction Code
(Instr. 8)		 4. Securities Acquired (A) or Disposed of (D)
(Instr. 3, 4 and 5)		 5. Amount of Securities Beneficially Owned Following Reported Transaction(s)
(Instr. 3 and 4)		 6. Ownership Form: Direct (D) or Indirect (I)
(Instr. 4)		 7. Nature of Indirect Beneficial Ownership
(Instr. 4)
Code V Amount (A) or (D) Price
Common Shares, $.01 par value per share (1) (2) (3)               9,348,044 I By Partnership
Common Shares, $.01 par value per share (3) 05/03/2006   A   569 A (5) 64,130 (4) D  

Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly.
Persons who respond to the collection of information contained in this form are not required to respond unless the form displays a currently valid OMB control number. SEC 1474 (9-02)

Table II - Derivative Securities Acquired, Disposed of, or Beneficially Owned
(e.g., puts, calls, warrants, options, convertible securities)
1. Title of Derivative Security
(Instr. 3)		 2. Conversion or Exercise Price of Derivative Security 3. Transaction Date (Month/Day/Year) 3A. Deemed Execution Date, if any (Month/Day/Year) 4. Transaction Code
(Instr. 8)		 5. Number of Derivative Securities Acquired (A) or Disposed of (D)
(Instr. 3, 4, and 5)		 6. Date Exercisable and Expiration Date
(Month/Day/Year)		 7. Title and Amount of Underlying Securities
(Instr. 3 and 4)		 8. Price of Derivative Security
(Instr. 5)		 9. Number of Derivative Securities Beneficially Owned Following Reported Transaction(s)
(Instr. 4)		 10. Ownership Form of Derivative Security: Direct (D) or Indirect (I)
(Instr. 4)		 11. Nature of Indirect Beneficial Ownership
(Instr. 4)
Code V (A) (D) Date Exercisable Expiration Date Title Amount or Number of Shares

Reporting Owners

Reporting Owner Name / Address Relationships
 Director  10% Owner  Officer  Other
BUNCE JOHN L JR
HELLMAN & FRIEDMAN LLC
ONE MARITIME PLAZA 12TH FLOOR
SAN FRANCISCO, CA 94111		   X      

Signatures

 /s/ Louis T. Petrillo Attorney in fact   05/05/2006
**Signature of Reporting Person Date

Explanation of Responses:

* If the form is filed by more than one reporting person, see Instruction 4(b)(v).
** Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).
(1) The security holders are HFCP IV (Bermuda), L.P., H&F International Partners IV-A (Bermuda), L.P., H&F International Partners IV-B (Bermuda), L.P. and H&F Executive Fund IV (Bermuda), L.P. (collectively, the Partnerships). H&F Investors IV (Bermuda), L.P. (HFI IV Bermuda) is the sole general partner of the Partnerships. H&F Corporate Investors IV (Bermuda), Ltd. (HFCI Bermuda) is the sole general partner of HFI IV Bermuda. A five member investment committee of HFCI Bermuda that has been formed by the shareholders of HFCI Bermuda (Investment Committee), has investment discretion over the securities. As a result, HFCI Bermuda and HFI IV Bermuda may be deemed to control the Partnerships. The members of the Investment Committee disclaim beneficial ownership, except to the extent of their respective indirect pecuniary interests in the Issuer.
(2) Mr. Bunce is a 9.9% shareholder of HFCI Bermuda, but is not a member of the Investment Committee. Other than the 7,001 Common Shares and the 3,300 options to purchase Common Shares granted to Mr. Bunce in consideration for his service as a director of the Issuer, the H&F entities described in Footnote 1 own 9,348,044 Common Shares.
(3) Mr. Bunce may be deemed to have an indirect pecuniary interest (within the meaning of Rule 16a-1 under the Securities Exchange Act of 1934) in an indeterminate portion of the Common Shares beneficially owned by the Partnerships. Mr. Bunce disclaims beneficial ownership of all Common Shares beneficially owned by these entities, including an aggregate of 7,001 Common Shares and 3,300 options to purchase Common Shares granted to Mr. Bunce in consideration for his service as a director of the Issuer, except to the extent of his indirect pecuniary interest in the Issuer held through such entities.
(4) Includes 7,001 Common Shares granted to Mr. Bunce in consideration for his service as a director of the Issuer, which are held for the benefit of the Partnerships. Mr. Bunce disclaims beneficial ownership of these 7,001 Common Shares except to the extent of his indirect pecuniary interest in the Issuer held through the Partnerships.
(5) Subject to the terms of the restricted share agreement, this represents restricted shares that will vest on May 2, 2007.

Note: File three copies of this Form, one of which must be manually signed. If space is insufficient, see Instruction 6 for procedure.

Potential persons who are to respond to the collection of information contained in this form are not required to respond unless the form displays a currently valid OMB number.