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

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(Print or Type Responses)

1. Name and Address of Reporting Person * JONES RALPH E III   2. Issuer Name and Ticker or Trading Symbol ARCH CAPITAL GROUP LTD. [ACGL] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) _____ Director _____ 10% Owner __X__ Officer (give title below) _____ Other (specify below) Chairman & CEO Arch Insur Gr (Last) (First) (Middle) C/O ARCH INSURANCE GROUP INC., ONE LIBERTY PLAZA 3. Date of Earliest Transaction (Month/Day/Year) 05/09/2008 (Street) NEW YORK, NY 10006 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               100 D   Common Shares, $.01 par value per share               166 I By spouse

Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly.
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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

Restricted Share Units

(1)

05/09/2008

A

8,350

(1)

(1)

Common Shares, $.01 par value per share

8,350

(1)

83,321

D

Stock Appreciation Right (2)

$ 69.3

05/09/2008

A

8,350

(2)

05/09/2018

Common Shares, $.01 par value per share

8,350

$ 0

8,350

D

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
JONES RALPH E III C/O ARCH INSURANCE GROUP INC. ONE LIBERTY PLAZA NEW YORK, NY 10006			Chairman & CEO Arch Insur Gr

Signatures

/s/ Ralph E. Jones III		05/12/2008
**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)	Subject to the applicable award agreement, represents restricted share units that vest in three equal annual installments on May 9th in each of 2009, 2010 and 2011; such award will settle in Issuer's common shares upon the termination of the Reporting Person's employment as specifically provided in the agreement.
(2)	The stock appreciation right will become exercisable in three equal annual installments, with the first installment becoming exercisable on May 9, 2009 and the next two installments on May 9, 2010 and May 9, 2011, subject to the terms of the applicable award agreement.

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