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
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(Print or Type Responses)
1. Name and Address of Reporting Person *
GRANDISSON MARC
  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)
Reinsur. Group Chairman & CEO
(Last)
(First)
(Middle)
WESSEX HOUSE, 45 REID STREET
3. Date of Earliest Transaction (Month/Day/Year)
05/11/2007
(Street)

HAMILTON, D0 HM 12
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 05/11/2007   A   10,450 (1) A (1) 103,808 D  
Common Shares, $.01 par value per share               220 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
Stock Appreciation Right (2) $ 71.12 05/11/2007   A   10,450     (2) 05/11/2017 Common Shares, $.01 par value per share 10,450 $ 0 10,450 D  

Reporting Owners

Reporting Owner Name / Address Relationships
 Director  10% Owner  Officer  Other
GRANDISSON MARC
WESSEX HOUSE, 45 REID STREET
HAMILTON, D0 HM 12
      Reinsur. Group Chairman & CEO  

Signatures

 /s/ Marc Grandisson   05/14/2007
**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) Represents restricted shares that vest in three equal annual installments on May 11th in each of 2008, 2009 and 2010, subject to the applicable award agreement.
(2) The stock appreciation right will become exercisable in three equal annual installments, with the first installment becoming exercisable on May 11, 2008 and the next two installments on May 11, 2009 and May 11, 2010, subject to the applicable award agreement.

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