Exhibit 4.1



                  [ ] CLASS A WARRANTS, EACH WARRANT ENTITLING
                     THE HOLDER TO PURCHASE ONE COMMON SHARE
                           OF ARCH CAPITAL GROUP LTD.


                             ARCH CAPITAL GROUP LTD.








THIS WARRANT (THE "WARRANT") AND THE UNDERLYING COMMON SHARES MAY NOT BE
TRANSFERRED, OFFERED OR SOLD EXCEPT (A) IN COMPLIANCE WITH THE PROVISIONS OF A
CERTAIN SUBSCRIPTION AGREEMENT AND A CERTAIN SHAREHOLDERS AGREEMENT EXECUTED IN
CONNECTION HEREWITH AND (B) PURSUANT TO (1) AN EFFECTIVE REGISTRATION STATEMENT
UNDER THE UNITED STATES SECURITIES ACT OF 1933, AS AMENDED, OR (2) AN APPLICABLE
EXEMPTION FROM REGISTRATION THEREUNDER. ANY SALE PURSUANT TO CLAUSE (B)(2) OF
THE PRECEDING SENTENCE MUST BE ACCOMPANIED BY AN OPINION OF WACHTELL, LIPTON,
ROSEN & KATZ, OR SUCH OTHER COUNSEL AS IS REASONABLY SATISFACTORY TO ARCH
CAPITAL GROUP LTD., TO THE EFFECT THAT SUCH EXEMPTION FROM REGISTRATION IS
AVAILABLE IN CONNECTION WITH SUCH SALE.








     ARCH CAPITAL GROUP LTD., a Bermuda exempted limited company (the
"Company"), hereby certifies that, for value received, [ ] (the "Holder"), or
its assigns, is entitled, subject to the terms set forth below, to purchase from
the Company, at any time and from time to time in whole or in part, an aggregate
of [ ] fully paid and nonassessable common shares, par value $.01 per share
("Common Shares"), of the Company during the period beginning on the date of
issuance hereof (the "Closing Date") and ending on September 19, 2002 (the
"Exercise Period").

     1. PURCHASE PRICE. Such Common Shares shall be purchased at a purchase
price per share, subject to the provisions of Paragraph 3 hereof, equal to
$20.00 (as adjusted in accordance with the terms hereof, the "Purchase Price").
The number and character of such Common Shares are subject to adjustment as
provided below, and the term "Common Shares" shall mean, unless the context
otherwise requires, the Common Shares or other securities or property at the
time deliverable upon the exercise of this Warrant.

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     2. EXERCISE OF WARRANT. The purchase rights evidenced by this Warrant shall
be exercised by the Holder surrendering this Warrant, with the form of
subscription at the end hereof duly executed by such Holder (the "Exercise
Notice"), to the Company at its offices, 20 Horseneck Lane, Greenwich,
Connecticut 06830, accompanied by payment as specified below of the aggregate
Purchase Price determined as of the Determination Date (as defined below) of the
Common Shares being purchased pursuant to such exercise. Payment of the
aggregate Purchase Price may be made, at the option of the Holder, (i) in cash,
(ii) by certified check or bank cashier's check payable to the order of the
Company in the amount of such Purchase Price, (iii) by delivering Common Shares
with an aggregate Market Price (as hereinafter defined) as of the day prior to
the Company's receipt of the Exercise Notice (the "Determination Date") equal to
the product of the Purchase Price and the number of Common Shares being
purchased, (iv) by the Company reducing, at the request of the Holder, the
number of Common Shares for which this Warrant is exercisable by a number of
Common Shares (the "Surrendered Stock") such that the product of (a) the Market
Price per Common Share as of the Determination Date less the Purchase Price in
effect on the Determination Date multiplied by (b) the Surrendered Stock equals
or exceeds the product of (x) the Purchase Price in effect on the Determination
Date and (y) the number of Common Shares being purchased, or any combination of
the methods of payment described in clauses (i) through (iv) above.

     2.1. Partial Exercise. This Warrant may be exercised for less than the full
number of Common Shares at the times called for hereby, in which case the number
of Common Shares receivable upon the exercise of this Warrant as a whole, the
sum payable upon the exercise of this Warrant as a whole, shall be
proportionately reduced. Upon any such partial exercise, the Company at its
expense will forthwith issue to the Holder hereof a new Warrant or Warrants of
like tenor for the number of Common Shares as to which rights have not been
exercised, such Warrant or Warrants to be issued in the name of the Holder
hereof or his nominee (upon payment by such Holder of any applicable transfer
taxes).

     2.2. Delivery of Certificates for Common Shares on Conversion. As soon as
practicable after the exercise of this Warrant and payment of the Purchase
Price, and in any event within ten (10) days thereafter, the Company, at its
expense, will cause to be issued in the name of and delivered to the Holder
hereof a certificate or certificates for the number of fully paid and
nonassessable Common Shares or other securities or property to which such Holder
shall be entitled upon such exercise, plus, in lieu of any fractional share to
which such Holder would otherwise be entitled, cash in an amount determined in
accordance with Paragraph 3.9 hereof. The Company agrees that the Common Shares
so received shall be deemed to be issued to the Holder as the record owner of
such Common Shares as of the close of business on the date on which this Warrant
shall have been surrendered and payment for such Common Shares made as
aforesaid.

     3. ANTI-DILUTION PROVISIONS AND OTHER ADJUSTMENTS. In order to prevent
dilution of the right granted hereunder, the Purchase Price shall be subject to
adjustment from time to time in accordance with this Paragraph 3. Upon each
adjustment of the Purchase Price pursuant to this Paragraph 3, the registered
holder hereof shall thereafter be entitled to acquire upon exercise of this
Warrant, at the Purchase Price resulting from such adjustment, the number of
shares of the Company's Common Shares obtainable by multiplying the Purchase
Price in effect immediately prior to such adjustment by the number of shares of
the Company's Common Shares acquirable upon


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                                      -3-


conversion thereof immediately prior to such adjustment and dividing the product
thereof by the Purchase Price resulting from such adjustment.

     3.1. Adjustment for Issue or Sale of Common Shares. Except as provided in
Paragraph 3.5 below, if and whenever on or after the date of issuance hereof the
Company shall issue or sell, or shall in accordance with subparagraphs (1) to
(8) of this Paragraph 3.1 inclusive, be deemed to have issued or sold any Common
Shares to any person for a consideration per share less than the Market Price
(or, in the case of an issuance or sale in connection with an underwritten
public offering, 99% of the Market Price less underwriting discounts and
commissions) in effect immediately prior to the time of such issue or sale, then
forthwith upon such issue or sale (each, a "Triggering Transaction"), the
Purchase Price shall, subject to subparagraphs (1) to (8) of this Paragraph 3.1,
be reduced to the Purchase Price (calculated to the nearest tenth of a cent)
determined by multiplying the Purchase Price in effect immediately prior to the
time of such Triggering Transaction by a fraction, the numerator of which shall
be the sum of (x) the product of the Number of Common Shares Deemed Outstanding
(as defined below) immediately prior to such Triggering Transaction multiplied
by the Market Price immediately prior to such Triggering Transaction plus (y)
the total amount, if any, received or receivable at any time by the Company as
consideration for the issuance or sale of such Common Shares, and the
denominator of which shall be the product of (x) the Number of Common Shares
Deemed Outstanding immediately after such Triggering Transaction, multiplied by
(y) the Market Price immediately prior to such Triggering Transaction; provided
that in the case of a sale of Common Shares pursuant to a purchase, underwriting
or similar agreement, the Market Price shall mean the Market Price in effect
upon the date such agreement is executed by the Company.

     For purposes of this Paragraph 3, the term "Number of Common Shares Deemed
Outstanding" at any given time shall mean the sum of (i) the number of Common
Shares outstanding at such time, and (ii) the number of Common Shares deemed to
be outstanding under subparagraphs (1) to (8) of this Paragraph 3, inclusive, at
such time. For purposes of this Paragraph 3, inclusive, at such time. For
purposes of this Paragraph 3, the term "Market Price" shall mean, as of any
date, (a) for any period during which a security shall be listed for trading on
a national securities exchange or on the Nasdaq Stock Market ("Nasdaq"), or (in
the case of non-United States securities) similar securities exchange, the
closing price per share of such security as of such day, or, in case no reported
sale occurs on such trading day, the mean of the reported closing bid and asked
prices per share for the prior five trading days ending on such day, (b) for any
period during which such security shall not be so listed, but when prices for
such security shall be reported by Nasdaq or similar system in the case of
non-U.S. securities, the mean of the most recent average bid and asked prices
per share as quoted by Nasdaq or such other system or (c) the market price per
share of such security as determined by the Board of Directors of the Company
(the "Board of Directors") as of the next preceding day, in the event neither
(a) nor (b) above shall be applicable, or in the event the Board of Directors
shall be in good faith determine that application of (a) or (b) would not result
in a fair determination of the Market Price.

     For purposes of determining the adjusted Purchase Price under this
Paragraph 3.1, the following subparagraphs (1) to (8), inclusive, shall be
applicable:


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                                      -4-


          (1) In case the Company at any time shall in any manner issue or sell
     (whether directly or by assumption in a merger or otherwise) any rights to
     subscribe for or to purchase, or any options for the purchase of, Common
     Shares or any other securities convertible into or exchangeable or
     exercisable for Common Shares (such rights or options being herein called
     "Options" and such convertible, exchangeable or exercisable shares or
     securities being herein called "Convertible Securities"), whether or not
     such Options or the right to convert, exercise or exchange any such
     Convertible Securities are immediately exercisable, and the price per share
     for which Common Shares are issuable upon exercise, conversion or exchange
     (determined by dividing (x) the total amount, if any, received or
     receivable by the Company as consideration for the issuing of such Options,
     plus the minimum aggregate amount of additional consideration payable to
     the Company upon the exercise of all such Options, by (y) the total maximum
     number of Common Shares issuable upon the exercise of such Options or the
     conversion or exchange of such Convertible Securities) shall be less than
     the Market Price (or, in the case of an issuance or sale in connection with
     an underwritten public offering, less than 99% of the Market Price less
     underwriting discounts and commissions), determined as of the date of such
     issuance or sale (or, in the case of an issuance or sale pursuant to a
     purchase, underwriting or similar agreement, the Market Price determined as
     of the date such agreement is executed by the Company), then the total
     maximum number of Common Shares issuable upon exercise of such Options or
     conversion or exchange of all such Convertible Securities shall (as of the
     date of the grant of such Option) be deemed to be outstanding and to have
     been issued and sold by the Company for such price per share. No adjustment
     of the Purchase Price shall be made upon exercise of such Options or
     conversion or exchange of such Convertible Securities, except as otherwise
     provided in subparagraph (3) below.

          (2) In case the Company at any time shall in any manner issue or sell
     (whether directly or by assumption in a merger or otherwise) any
     Convertible Securities, whether or not the rights to exchange, exercise or
     convert thereunder are immediately exercisable, and the price per share for
     which Common Shares are issuable upon such conversion, exercise or exchange
     (determined by dividing (x) the total amount received or receivable by the
     Company as consideration for the issue or sale of such Convertible
     Securities, plus the minimum aggregate amount of additional consideration,
     if any, payable to the Company upon the conversion or exchange thereof, by
     (y) the total maximum number of Common Shares issuable upon the conversion
     or exchange of all such Convertible Securities) shall be less than the
     Market Price (or, in the case of an issuance or sale in connection with an
     underwritten public offering, less than 99% of the Market Price less
     underwriting discounts and commissions), determined as of the date of such
     issuance or sale (or, in the case of an issuance or sale pursuant to a
     purchase, underwriting or similar agreement, the Market Price determined as
     of the date such agreement is executed by the Company), then the total
     maximum number of Common Shares issuable upon conversion or exchange of all
     such Convertible Securities shall (as of the date of the issue or sale of
     such Convertible Securities) be deemed to be outstanding and to have been
     issue and sold by the Company for such price per share. No adjustment of
     the Purchase Price shall be made upon the actual issue of such Common
     Shares upon exercise of the rights to exchange or convert under such
     Convertible Securities, except as otherwise provided in subparagraph (3)
     below.


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                                      -5-


          (3) If the exercise price provided for in any Options referred to in
     subparagraph (1), the additional consideration, if any, payable upon the
     conversion or exchange of any Convertible Securities referred to in
     subparagraph (1) or (2), or the rate at which any Convertible Securities
     referred to in subparagraph (1) or (2) are convertible into or exchangeable
     for Common Shares, shall change at any time (other than under or by reason
     of provisions designed to protect against dilution of the type set forth in
     Paragraph 3.1 or 3.3), the Purchase Price in effect at the time of such
     change shall forthwith be readjusted to the Purchase Price which would have
     been in effect at the time had such Options or Convertible Securities still
     outstanding provided for such changed purchase price, additional
     consideration or conversion or exchange rate, as the case may be, at the
     time initially granted, issued or sold. If the exercise price provided for
     in any Option referred to in subparagraph (1), the additional
     consideration, if any, payable upon the conversion or exchange of any
     Convertible Securities referred to in subparagraph (1) or (2), or the rate
     at which any Convertible Securities referred to in subparagraph (1) or (2)
     are convertible into or exchangeable for Common Shares, shall be reduced at
     any time under or by reason of provisions with respect thereto designed to
     protect against dilution, then the Purchase Price then in effect hereunder
     shall forthwith be adjusted to such respective amount as would have been
     obtained had such Option or Convertible Security never been issued as to
     such Common Shares and had adjustments been made upon the issuance of
     Common Shares delivered as aforesaid, but only if as a result of such
     adjustment the Purchase Price then in effect hereunder is hereby reduced
     and provided that there shall be no duplication of any adjustments
     otherwise made in accordance with the terms hereof.

          (4) On the expiration of any Option or the termination of any right to
     convert or exchange any Convertible Securities, the Purchase Price then in
     effect hereunder shall forthwith be increased to the Purchase Price which
     would have been in effect at the time of such expiration or termination had
     such Option or Convertible Securities, to the extent outstanding
     immediately prior to such expiration or termination, never been issued.

          (5) In case any Options shall be issued in connection with the issue
     or sale of other securities of the Company, together comprising one
     integral transaction in which no specific consideration is allocated to
     such Options by the parties thereto, such Options shall be deemed to have
     been issued without consideration.

          (6) In case any Common Shares, Options or Convertible Securities shall
     be issued or sold or deemed to have been issued or sold for cash, the
     consideration received therefor shall be deemed to be the amount received
     by the Company therefor. In case any Common Shares, Options or Convertible
     Securities shall be issued or sold for a consideration other than cash, the
     amount of the consideration other than cash received by the Company shall
     be the fair value of such consideration as determined in good faith by the
     Board of Directors.

          (7) The number of Common Shares outstanding at any given time shall
     not include shares owned or held by or for the account of the Company, but
     the disposition of any


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                                      -6-


     shares so owned or held shall be considered an issue or sale of Common
     Shares for the purpose of this Paragraph 3.1.

          (8) In case the Company shall declare a dividend or make any other
     distribution upon the stock of the Company payable in Common Shares,
     Options or Convertible Securities, then in such case any Common Shares,
     Options or Convertible Securities, as the case may be, issuable in payment
     of such dividend or distribution shall be deemed to have been issued or
     sold without consideration.

     3.2. Determination of Date of Issuance or Sale of Common Shares. For
purposes of Paragraph 3.1, in case the Company shall take a record of the
holders of its Common Shares for the purpose of determining holders entitled (x)
to receive a dividend or other distribution payable in Common Shares, Options or
Convertible Securities, or (y) to subscribe for or purchase Common Shares,
Options or Convertible Securities, then such record date shall be deemed to have
been issued or sold upon the declaration of such dividend or the making of such
other distribution or the date of the granting of such right or subscription or
purchase, as the case may be.

     3.3. Subdivisions and Combinations. In case the Company shall at any time
subdivide (other than by means of a dividend payable in Common Shares covered by
subparagraph 3.1(8)) its outstanding Common Shares into a greater number of
shares, the Purchase Price in effect immediately prior to such subdivision shall
be appropriately reduced, and, conversely, in case the outstanding Common Shares
of the Company shall be combined into a smaller number of shares, the Purchase
Price in effect immediately prior to such combination shall be proportionately
increased.

     3.4. Reorganization, Reclassification, Consolidation, Merger or Sale of
Assets. If any capital reorganization or reclassification of the shares of the
Company, or consolidation or merger of the Company with another corporation, or
the sale of all or substantially all of its assets to another corporation shall
be effected in such a way that holders of Common Shares shall be entitled to
receive stock, securities, cash or other property with respect to or in exchange
for Common Shares, then, as a condition of such reorganization,
reclassification, consolidation, merger or sale, lawful and adequate provision
shall be made whereby the Holder of this Warrant shall have the right to acquire
and receive upon exercise hereof such common stock, securities, cash or other
property issuable or payable (as part of the reorganization, reclassification,
consolidation, merger or sale) with respect to or in exchange for such number of
outstanding Common Shares of the Company as would have been received upon
exercise of this Warrant at the Purchase Price then in effect. The Company will
not effect any such consolidation, merger or sale unless prior to the
consummation thereof the successor corporation (if other than the Company)
resulting from such consolidation or merger or the corporation purchasing such
assets shall assume by written instrument, mailed or delivered to the Holder of
this Warrant at the last address of such Holder appearing on the books of the
Company, the obligation to deliver to such holder such common stock, securities
or assets as, in accordance with the foregoing provisions, such Holder may be
entitled to purchase. In the event that pursuant to the terms of this Paragraph
3.4, this Warrant becomes exercisable for securities other than Common Shares,
then the provisions of Section 3 shall apply to such securities as though such
securities were Common Shares. If a purchase, tender or exchange offer is made
to and accepted by the holders of more than 50% of the outstanding Common Shares
of the Company, the Company shall not effect any


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                                      -7-


consolidation, merger or sale with the person having made such offer or with any
Affiliate of such person unless prior to the consummation of such consolidation,
merger or sale the holder of this Warrant shall have been given a reasonable
opportunity to then elect to receive upon the exercise of this Warrant either
the common shares, securities or assets then issuable with respect to the Common
Shares of the Company or the common shares, securities or assets, or the
equivalent, issued to previous holders of the Common Shares in accordance with
such offer. For purposes hereof the term "Affiliate" with respect to any given
person shall mean any person controlling, controlled by or under common control
with the given person.

     3.5. No Adjustment for Exercise of Certain Options, Warrants, Etc. The
provisions of this Section 3 shall not apply to any Common Shares issued,
issuable or deemed outstanding under subparagraphs (1) to (8) of paragraph 3.1,
inclusive: (i) to any person pursuant to any stock option, stock purchase or
similar plan or arrangement for the benefit of employees or directors of the
Company or its subsidiaries; provided that any Common Shares issued pursuant to
any such plan or arrangement (in excess of 1,700,000 shares) shall be approved
by the Board of Directors or a duly organized committee thereof, it being
further provided that, with respect to Class A Warrants exercised by the Initial
Investors or their Affiliates (as defined in the Registration Statement filed by
the Company in connection with the Company's public offering of its Common
Shares), this Section 3 shall apply with respect to any Common Shares issued
pursuant to any such plan or arrangement in excess of 1,700,000 shares (ii)
pursuant to options, warrants and conversion rights in existence on the date of
issuance hereof or (iii) pursuant to the exercise of any Class A Warrants or
Class B Warrants described in the Company's prospectus relating to the initial
public offering of its Common Shares.

     3.6. Notices of Record Date, Etc. In the event that:

          (1) the Company shall declare any cash dividend upon its Common
     Shares, or

          (2) the Company shall declare any dividend upon its Common Shares
     payable in common shares or make any special dividend or other distribution
     to the holders of its Common Shares, or

          (3) the Company shall offer for subscription pro rata to the holders
     of its Common Shares any additional common shares of any class or other
     rights, or

          (4) there shall be any capital reorganization or reclassification of
     the shares of the Company, including any subdivision or combination of its
     outstanding Common Shares, or consolidation or merger of the Company with,
     or sale of all or substantially all of its assets to, another corporation,
     or

          (5) there shall be a voluntary or involuntary dissolution, liquidation
     or winding up of the Company;

then, in connection with such event, the Company shall give to the Holder of
this Warrant:


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     (i)  at least ten (10) days' prior written notice of the date on which the
          books of the Company shall close or a record shall be taken for such
          dividend distribution or subscription rights or for determining rights
          to vote in respect of any such reorganization, reclassification,
          consolidation, merger, sale, dissolution, liquidation or winding up;
          and

     (ii) in the case of any such reorganization, reclassification,
          consolidation, merger, sale, dissolution, liquidation or winding up,
          at least ten (10) days prior written notice of the date when the same
          shall take place.

Such notice in accordance with the foregoing clause (i) shall also specify, in
the case of any such dividend, distribution or subscription rights, the date on
which the holders of Common Shares shall be entitled thereto, and such notice in
accordance with the foregoing clause (ii) shall also specify the date on which
the holders of Common Shares shall be entitled to exchange their Common Shares
for securities or other property deliverable upon such reorganization,
reclassification, consolidation, merger, sale, dissolution, liquidation or
winding up, as the case may be. Each such written notice shall be given by first
class mail, postage prepaid, addressed to the Holder of this Warrant at the
address of such Holder as shown on the books of the Company.

     3.7. Adjustments for Other Distributions. If at any time or from time to
time on or after the date of issuance hereof, the Company shall distribute,
grant or issue to all holders of its Common Shares any of its assets or debt
securities or any rights or warrants to purchase assets or securities of the
Company (including securities or cash, but excluding (x) distributions covered
by Section 3.1 or (y) cash dividends or other cash distributions that are paid
out of consolidation current net earnings or earnings retained in the business
as shown on the books of the Company unless such cash distributions in any
twelve month period exceed 3.00% of the average Market Price of the Common
Shares for the fifteen (15) trading days ending on the first day of such twelve
month period) (collectively, the "Purchase Rights"), then the Holder of this
Warrant shall be entitled to, at its option:

     (i)  have the Purchase Price reduced to the Purchase Price (calculated to
          the nearest tenth of a cent) determined by multiplying the Purchase
          Price in effect immediately prior to the time of distribution of such
          Purchase Rights by a fraction, the numerator of which shall be the
          difference between (x) the Market Price immediately prior to such
          distribution and (y) the fair market value of the assets, securities,
          rights or warrants applicable to one Common Share (which fair market
          value shall be determined by the Company in accordance with generally
          accepted accounting principals) and the denominator of which shall be
          the Market Price immediately prior to such distribution; provided that
          in the case of a distribution, grant or issuance pursuant to a
          purchase, underwriting or similar agreement, the Market Price shall
          mean the Market Price in effect upon the date such agreement is
          executed by the Company; or

     (ii) acquire (within thirty (30) days after the later to occur of the
          initial exercise date of such Purchase Rights or receipt by such
          Holder of the notice concerning Purchase Rights to which such Holder
          shall be entitled under Para-


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                                      -9-


          graph 3.6) and upon the terms applicable to such Purchase Rights
          either: (x) the aggregate Purchase Rights which such Holder could have
          acquired if it had held the number of Common Shares acquirable upon
          exercise of this Warrant immediately before the grant, issuance or
          sale of such Purchase Rights; provided that if any Purchase Rights
          were distributed to holders of Common Shares without the payment of
          additional consideration by such holders, corresponding Purchase
          Rights shall be distributed to the exercising holder of this Warrant
          as soon as possible after such exercise and it shall not be necessary
          for the exercising holder of this Warrant specifically to request
          delivery of such rights; or (y) in the event that any such Purchase
          Rights shall have expired or shall expire prior to the end of said
          thirty (30) day period, the number of Common Shares or the amount of
          property which such Holder could have acquired upon such exercise at
          the same time or times at which the Company granted, issued or sold
          such expired Purchase Rights.

     3.8. Adjustment by Board of Directors. If any event occurs as to which the
provisions of this Section 3 are not strictly applicable or if strictly
applicable would not fairly protect the rights of the Holder of this Warrant in
accordance with the essential intent and principles of such provisions, then the
Board of Directors shall make an adjustment in the application of such
provisions, in accordance with such essential intent and principles, so as to
protect such rights as aforesaid, but in no event shall any adjustment have the
effect of increasing the Purchase Price as otherwise determined pursuant to any
of the provisions of this Section 3 except in the case of a combination of
shares of a type contemplated in Paragraph 3.3 and then in no event to an amount
larger than the Purchase Price as adjusted pursuant to Paragraph 3.3.

     3.9. Fractional Shares. The company shall not issue fractions of Common
Shares upon exercise of this Warrant or scrip in lieu thereof. If any fraction
of a Common Share would, except for the provisions of this Paragraph 3.9, be
issuable upon exercise of this Warrant, the company shall in lieu thereof pay to
the person entitled thereto an amount in cash equal to the product of such
fraction, calculated to the nearest one-hundredth (1/100), and the Market Price
of a Common Share as of such date of exercise.

     3.10. Officers' Statement as to Adjustments. Whenever the Purchase Price
shall be adjusted as provided in this Section 3, the Company shall forthwith
file at the office designated for the exercise of this Warrant a statement,
signed by the chairman of the Board, the President, any Vice President or the
Treasurer of the Company, showing in reasonable detail the facts requiring such
adjustment and the Purchase Price that will be effective after such adjustment.
The Company shall also cause a notice setting forth any such adjustments to be
sent by mail, first class, postage prepaid, to the record holder of this warrant
at his or its address appearing on the Warrant register of the Company. If such
notice relates to an adjustment resulting from an event referred to in Paragraph
3.6, such notice shall be included as part of the notice required to be mailed
and published under the provisions of Paragraph 3.6.

     4. NO DILUTION OR IMPAIRMENT. The Company will not, by amendment of its
charter or through reorganization, reclassification, consolidation,
amalgamation, merger, dissolution,


<PAGE>
                                      -10-


sale of assets or any other voluntary action, avoid or seek to avoid the
observance or performance of any of the terms of this Warrant, but will at all
times in good faith assist in the carrying out of all such terms and in the
taking of all such action as may be necessary or appropriate in order to protect
the rights of the Holder hereof against dilution or other impairment. Without
limiting the generality of the foregoing, the Company will not increase the par
value of any Common Share receivable upon the exercise of this Warrant above the
amount payable therefor upon such exercise, and at all times will take all such
action as may be necessary or appropriate in order that the Company may validly
and legally issue fully paid and nonassessable Common Shares upon the exercise
of this Warrant.

     5. RESERVATION OF COMMON SHARES, ETC., ISSUABLE UPON EXERCISE OF WARRANTS.
The Company shall at all times reserve and keep available out of its authorized
but unissued Common Shares, solely for issuance and delivery upon the exercise
of this Warrant and other similar warrants, such number of its duly authorized
Common Shares as from time to time shall be issuable upon the exercise of this
Warrant and all other similar warrants at the time outstanding.

     6. REPLACEMENT OF WARRANT. Upon receipt of evidence reasonably satisfactory
to the Company of the loss, theft, destruction or mutilation of this Warrant and
(in the case of loss, theft or destruction) upon delivery of an indemnity
agreement (with surety if reasonably required) in an amount reasonably
satisfactory to it, or (in the case of mutilation) upon surrender and
cancellation thereof, the Company will issue, in lieu thereof, a new Warrant of
like tenor.

     7. REMEDIES. The Company stipulates that the remedies at law of the Holder
of this Warrant in the event of any default by the Company in the performance of
or compliance with any of the terms of this Warrant are not and will not be
adequate, and that the same may be specifically enforced.

     8. NEGOTIABILITY, ETC. This Warrant is issued upon the following terms, to
all of which each taker or owner hereof consents and agrees:

     (a)  Nether this Warrant, the Common Shares underlying this Warrant (the
          "Underlying Stock") nor the rights of the Holder hereunder may be
          transferred except in compliance with the provisions of a certain
          Subscription Agreement and a certain Shareholders Agreement executed
          in connection with the issuance of this Warrant, copies of which are
          on file at the principal office of the Company.

          The provisions of this Section 8 shall be binding upon any transferee
          of this Warrant and upon each holder of Underlying Stock.

     (b)  Subject to the limitation described in this Section 8, title to this
          Warrant may be transferred by endorsement (by the Holder hereof
          executing the form of assignment at the end hereof including guaranty
          of signature) and delivery in the same manner as in the case of a
          negotiable instrument transferable by endorsement and delivery.


<PAGE>
                                      -11-


     (c)  Any person in possession of this Warrant properly endorsed and, if not
          the original holder hereof, to whom possession was transferred in
          accordance with the provisions was transferred in accordance with the
          provisions of clauses (a) and (b) of this Section 8 is authorized to
          represent himself as absolute owner hereof and is granted power to
          transfer absolute title hereto by endorsement and delivery hereof to a
          bona fide purchaser hereof for value; each prior taker or owner waives
          and renounces all of his equities or rights in this Warrant in favor
          of every such bona fide purchaser, and every such bona fide purchaser
          shall acquire title hereto and to all rights represented hereby.

     (d)  Until this Warrant is transferred on the books of the Company, the
          Company may treat the registered Holder of this Warrant as the
          absolute owner hereof for all purposes without being affected by any
          notice to the contrary.

     (e)  The Company shall not be required to pay any U.S. federal or state
          transfer tax or charge that may be payable in respect of any transfer
          involved in the transfer or delivery of this Warrant or the issuance
          or conversion or delivery of certificates for Common Shares in a name
          other than that of the registered Holder of this warrant or to issue
          or deliver any certificates for Common Shares upon the exercise of
          this Warrant until any and all such taxes and charges shall have been
          paid by the Holder of this Warrant or until it has been established to
          the Company's satisfaction that no such tax or charge is due.

     9. NO RIGHTS TO VOTE OR RECEIVE DIVIDENDS OR OTHER DISTRIBUTIONS. Prior to
the exercise of this Warrant, the Holder hereof shall not be entitled to any
rights of a shareholder of the Company with respect to Common Shares for which
this Warrant shall be exercisable, including, without limitation, the right to
vote, to receive dividends or other distributions or to exercise any preemptive
rights, and shall not be entitled to receive any notice of any proceedings of
the Company, except as provided herein.

     10. MAILING OF NOTICES, ETC. All notices and other communications from the
Company to the Holder of this Warrant shall be mailed by first-class certified
mail, postage prepaid, to the address furnished to the Company in writing by the
last Holder of this Warrant who shall have furnished an address to the Company
in writing.

     11. CHANGE, WAIVER, ETC. The terms of this Warrant may not be changed,
waived, discharged or terminated orally but only by an instrument in writing
signed by the Holder of this Warrant against which enforcement of the change,
waiver, discharge or termination is sought.

     12. GOVERNING LAW. This Warrant shall be governed by and construed in
accordance with the laws of Bermuda, without regard to principles regarding
conflicts of laws.



<PAGE>
                                       S-1


                                ARCH CAPITAL GROUP LTD.


                                By:
                                       -------------------------------------
                                       Name:
                                       Title:

Dated:

Attest:





<PAGE>



                  [To be signed only upon exercise of Warrant]


To Arch Capital Group Ltd.

     The undersigned, the Holder of the within Warrant, hereby irrevocably
elects to exercise the purchase right represented by such Warrant for, and to
purchase thereunder, ________________ Common Shares of Arch Capital Group Ltd.
and herewith makes payment of $_________ therefor and/or requests that the
number of Common Shares for which the within Warrant is exercisable to reduced
by __________ Common Shares (in addition to the Common Shares being purchased)
and/or delivers _________ Common Shares, the aggregate of such payment being
equal to the aggregate purchase price for the Common Shares being purchased, and
requests that the certificates for the Common Shares being purchased be issued
in the name of, and be delivered to, _____________, whose address is
----------------.

Dated:


_______________________________

                                 ______________________________________________
                                 (Signature must conform in all respects to
                                 name of Holder as specified on the face of the
                                 Warrant)


                                 ______________________________________________
                                                      Address


<PAGE>



                  [To be signed only upon transfer of Warrant]


     FOR VALUE RECEIVED, the undersigned hereby sells, assigns and transfers
unto ______________ the within Warrant and appoints _______________ attorney to
transfer said right on the books of Arch Capital Group Ltd. with full power of
substitution in the premises.

Dated:


_____________________________


                                _______________________________________________
                                (Signature must conform in all respects to
                                name of Holder as specified on the face of the
                                Warrant)


                                _______________________________________________
                                                   Address



In the presence of

_____________________________