Ownership Submission
FORM 3
 UNITED STATES SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

INITIAL STATEMENT OF 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 *
  McElroy David
 2. Date of Event Requiring Statement (Month/Day/Year)
07/25/2012		 3. Issuer Name and Ticker or Trading Symbol
ARCH CAPITAL GROUP LTD. [ACGL]
(Last)
(First)
(Middle)
300 PLAZA THREE, 3RD FLOOR		 4. 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
 5. If Amendment, Date Original Filed(Month/Day/Year)
07/25/2012
(Street)

JERSEY CITY, NJ 07311		 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 Beneficially Owned
1.Title of Security
(Instr. 4)		 2. Amount of Securities Beneficially Owned
(Instr. 4)		 3. Ownership Form: Direct (D) or Indirect (I)
(Instr. 5)		 4. Nature of Indirect Beneficial Ownership
(Instr. 5)
Common Shares, $.0033 par value per share 33,743 (5)
D
 

Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly. SEC 1473 (7-02)
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Table II - Derivative Securities Beneficially Owned (e.g., puts, calls, warrants, options, convertible securities)
1. Title of Derivative Security
(Instr. 4)		 2. Date Exercisable and Expiration Date
(Month/Day/Year)		 3. Title and Amount of Securities Underlying Derivative Security
(Instr. 4)		 4. Conversion or Exercise Price of Derivative Security 5. Ownership Form of Derivative Security: Direct (D) or Indirect (I)
(Instr. 5)		 6. Nature of Indirect Beneficial Ownership
(Instr. 5)
Date Exercisable Expiration Date Title Amount or Number of Shares
Stock Appreciation Right   (1) 06/08/2019 Common Shares, $.0033 par value per share 22,500 $ 19.347 D  
Stock Appreciation Right   (2) 05/05/2020 Common Shares, $.0033 par value per share 13,500 $ 25.01 D  
Stock Appreciation Right   (3) 05/06/2021 Common Shares, $.0033 par value per share 4,200 $ 33.913 D  
Stock Appreciation Right   (4) 05/09/2022 Common Shares, $.0033 par value per share 2,400 $ 38.58 D  

Reporting Owners

Reporting Owner Name / Address Relationships
Director 10% Owner Officer Other
McElroy David
300 PLAZA THREE, 3RD FLOOR
JERSEY CITY, NJ 07311		       Chairman & CEO Arch Insur Gr  

Signatures

/s/ David McElroy 07/31/2012
**Signature of Reporting Person Date

Explanation of Responses:

* If the form is filed by more than one reporting person, see Instruction 5(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 stock appreciation right became exercisable in three equal annual installments, with the first installment became exercisable on June 8, 2010 and the next two installments on June 8, 2011 and June 8, 2012.
(2) The stock appreciation right will become exercisable in three equal annual installments, with the first installment becoming exercisable on May 5, 2011 and the next two installments on May 5, 2012 and May 5, 2013.
(3) The stock appreciation right will become exercisable in three equal annual installments, with the first installment becoming exercisable on May 6, 2012 and the next two installments on May 6, 2013 and May 6, 2014.
(4) The stock appreciation right will become exercisable in three equal annual installments, with the first installment becoming exercisable on May 9, 2013 and the next two installments on May 9, 2014 and May 9, 2015.
(5) 4,500 of such shares are restricted and subject to vest on May 5, 2013; 2,800 of such shares are restricted and subject to vest in two equal annual installments on May 6, 2013 and May 6, 2014; 2,400 of such shares are restricted and subject to vest in three equal annual installments on May 9, 2013, May 9, 2014 and May 9, 2015.

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