Exhibit 99.1
[LOGO] Endurance

                                           Contacts
                                           Massa B. Cressall, Investor Relations
                                           Phone: (441) 278-0988
                                           Email: mcressall@endurance.bm

ENDURANCE SPECIALTY HOLDINGS EARNS $100.9 MILLION IN FIRST QUARTER 2004; NET
INCOME INCREASES 97%

PEMBROKE, Bermuda - April 26, 2004 - Endurance Specialty Holdings Ltd.
(NYSE:ENH), today reported first quarter 2004 net income of $100.9 million or
$1.47 per diluted share versus net income of $51.2 million or $0.86 per diluted
share in the first quarter of 2003. In the first quarter of 2004, operating
income, which excludes after-tax realized investment gains and losses and
foreign exchange gains and losses, was $98.7 million or $1.44 per diluted share,
91.4% higher than for the first quarter of 2003. Annualized operating return on
average equity during the first quarter of 2004 was 23.2%.

Kenneth J. LeStrange, Chairman and Chief Executive Officer, commented,
"Generating $100 million in net income for the quarter was another milestone
achievement for Endurance. We have again demonstrated the ability of our
business platform to deliver superior results."

He continued, "Each of our business segments reported strong results. Our U.S.
and U.K. subsidiaries made significant progress during their first renewal
season as fully staffed companies. We are now increasingly seeing the benefits
of key strategic decisions made during the Company's formation to focus across a
number of highly attractive business lines and key geographies."

Gross premiums written were $720.6 million for the quarter ended March 31, 2004,
an increase of 99.0% from the $362.1 million in gross premiums written for the
first quarter of 2003. The growth in written premiums was a result of the
renewal of business obtained from the Hart Re portfolio acquisition during the
second quarter of 2003 and growth from the Company's U.S. and U.K. subsidiaries
which commenced operations at the beginning of 2003.

Earned premiums in the quarter were $415.8 million, an increase of 119.3% from
the first quarter of 2003.

The combined ratio was 81.6% in the first quarter of 2004 compared to 83.4% in
the first quarter of 2003. The loss ratio was 53.4% in the quarter compared to
54.9% in the first quarter of 2003. The Company benefited from a low level of
loss activity in the quarter.

At March 31, 2004, the Company's GAAP shareholder's equity was $1.8 billion or
$25.51 per diluted share, up 15.6% from March 31, 2003, and up 6.2% in the
quarter. Total assets were $4.1 billion and cash and invested assets were $3.0
billion, up almost $1.8 billion since the Company's formation in December 2001.
Net operating cash flow was $270 million in the first quarter of 2004. The
duration of the investment portfolio was 2.74 years reflecting the Company's
strategy of holding more cash and cash equivalents during relatively
unattractive interest rate environments.

Endurance will host a conference call on Tuesday, April 27, 2004 at 8:30 AM
Eastern to discuss its financial results. The conference call can be accessed
via telephone by dialing (800) 289-0730 (toll-free) or


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(913) 981-5509 (international). A telephone replay of the conference call will
be available through May 11, 2004 by dialing (888) 203-1112 (toll-free) or (719)
457-0820 (international) and entering the pass code: 416060.

The public may access a live broadcast of the conference call at the "Investors"
section of Endurance's website, www.endurance.bm.

A copy of the Company's financial supplement for the first quarter of 2004 will
be available on the Company's website at http://www.endurance.bm shortly after
the release of earnings.

Operating income and annualized operating return on average equity are non-GAAP
measures. A reconciliation of these measures to net income is provided on the
attached table entitled "Reconciliation".

About Endurance Specialty Holdings

Endurance Specialty Holdings Ltd. is a global provider of property and casualty
insurance and reinsurance. Through its operating subsidiaries, Endurance
currently writes property per risk treaty reinsurance, property catastrophe
reinsurance, casualty treaty reinsurance, property individual risks, casualty
individual risks, and other specialty lines. Endurance's operating subsidiaries
have been assigned a group rating of A (Excellent) from A.M. Best and A- from
Standard & Poor's. Endurance's headquarters are located at Wellesley House, 90
Pitts Bay Road, Pembroke HM 08, Bermuda and its mailing address is Endurance
Specialty Holdings, Suite No. 784, No. 48 Par-la-Ville Road, Hamilton HM 11,
Bermuda. For more information about Endurance, please visit
http://www.endurance.bm.

Safe Harbor for Forward-Looking Statements

Some of the statements in this press release may include forward-looking
statements which reflect our current views with respect to future events and
financial performance. Such statements may include forward-looking statements
both with respect to us in general and the insurance and reinsurance sectors
specifically, both as to underwriting and investment matters. Statements which
include the words "expect," "intend," "plan," "believe," "project,"
"anticipate," "seek," "will," and similar statements of a future or
forward-looking nature identify forward-looking statements in this press release
for purposes of the U.S. federal securities laws or otherwise. We intend these
forward-looking statements to be covered by the safe harbor provisions for
forward-looking statements in the Private Securities Litigation Reform Act of
1995.

All forward-looking statements address matters that involve risks and
uncertainties. Accordingly, there are or may be important factors that could
cause actual results to differ from those indicated in the forward-looking
statements. These factors include, but are not limited to, competition, possible
terrorism or the outbreak of war, the frequency or severity of unpredictable
catastrophic events, changes in demand for insurance or reinsurance, rating
agency actions, uncertainties in our reserving process, a change in our tax
status, acceptance of our products, the availability of reinsurance or
retrocessional coverage, retention of key personnel, political conditions,
changes in accounting policies, changes in general economic conditions and other
factors described in our Annual Report on Form 10-K for the year ended December
31, 2003.

Forward-looking statements speak only as of the date on which they are made, and
we undertake no obligation publicly to update or revise any forward-looking
statement, whether as a result of new information, future developments or
otherwise.


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                        ENDURANCE SPECIALTY HOLDINGS LTD.

                           CONSOLIDATED BALANCE SHEETS

                       AT MARCH 31, 2004 AND DECEMBER 31, 2003

       (in thousands of United States dollars, except per share amounts)



                                                                   March 31,     December 31,
                                                                     2004            2003
                                                                  ----------     ------------
Assets                                                            (UNAUDITED)      (AUDITED)
                                                                            
Cash and cash equivalents                                         $  274,001      $  150,923
Fixed maturity investments available for sale, at fair value       2,706,914       2,523,309
Premiums receivable, net                                             781,463         518,539
Deferred acquisition costs                                           241,960         183,387
Securities lending collateral                                         30,620              --
Prepaid reinsurance premiums                                           4,643           2,335
Accrued investment income                                             23,515          20,434
Intangible assets                                                     31,463          32,407
Other assets                                                          32,938          27,630
                                                                  ----------      ----------
Total Assets                                                      $4,127,517      $3,458,964
                                                                  ==========      ==========

Liabilities
Reserve for losses and loss expenses                              $1,019,318      $  833,158
Reserve for unearned premiums                                      1,129,102         824,685
Securities lending payable                                            30,620              --
Reinsurance balances payable                                          25,324          23,977
Bank debt                                                            103,029         103,029
Net payable for investments purchased                                 24,705              --
Other liabilities                                                     32,316          29,300
                                                                  ----------      ----------
Total Liabilities                                                  2,364,414       1,814,149
                                                                  ----------      ----------

Shareholders' Equity
Common shares
   63,943,486 issued and outstanding (2003 - 63,912,000)              63,943          63,912
Additional paid-in capital                                         1,192,908       1,189,570
Accumulated other comprehensive income                                71,699          46,068
Retained earnings                                                    434,553         345,265
                                                                  ----------      ----------
Total Shareholders' Equity                                         1,763,103       1,644,815
                                                                  ----------      ----------

Total Liabilities and Shareholders' Equity                        $4,127,517      $3,458,964
                                                                  ==========      ==========

Book Value per Common Share
Dilutive common shares outstanding                                    69,121          68,445
Diluted book value per common share                               $    25.51      $    24.03
                                                                  ==========      ==========



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                        ENDURANCE SPECIALTY HOLDINGS LTD.

                   UNAUDITED CONSOLIDATED STATEMENTS OF INCOME

            FOR THE QUARTERS ENDED MARCH 31, 2004 AND MARCH 31, 2003

       (in thousands of United States dollars, except per share amounts)



                                                                                Quarter Ended      Quarter Ended
                                                                                March 31, 2004     March 31, 2003
                                                                                --------------     --------------
                                                                                              
Revenues
Gross premiums written                                                           $    720,631       $    362,115
                                                                                 ============       ============
Net premiums written                                                                  717,007            360,054
Change in unearned premiums                                                          (301,181)          (170,401)
                                                                                 ------------       ------------
Net premiums earned                                                                   415,826            189,653
Net investment income                                                                  24,675             14,356
Net realized gains on sales of investments                                              5,176              4,404
                                                                                 ------------       ------------
Total Revenues                                                                        445,677            208,413
                                                                                 ------------       ------------

Expenses
Losses and loss expenses                                                              222,009            104,145
Acquisition expenses                                                                   85,518             34,560
General and administrative expenses                                                    31,767             19,466
Amortization of intangibles                                                               944                405
Net foreign exchange losses (gains)                                                     3,159             (2,506)
Interest expense                                                                          828              1,207
                                                                                 ------------       ------------
Total expenses                                                                        344,225            157,277
                                                                                 ------------       ------------

Income before income taxes                                                            101,452             51,136
Income tax (expense) benefit                                                             (580)                65
                                                                                 ------------       ------------
Net income                                                                            100,872             51,201
                                                                                 ============       ============

Per share data
Weighted average number of common and common equivalent shares outstanding:
Basic                                                                              64,083,528         58,457,745
Diluted                                                                            68,554,793         59,671,510
Basic earnings per share                                                         $       1.57       $       0.88
                                                                                 ============       ============
Diluted earnings per share                                                       $       1.47       $       0.86
                                                                                 ============       ============


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                        ENDURANCE SPECIALTY HOLDINGS LTD.

                          CONSOLIDATED FINANCIAL RATIOS

            FOR THE QUARTERS ENDED MARCH 31, 2004 AND MARCH 31, 2003



                                                 Quarter Ended March         Quarter Ended March
                                                      31, 2004                     31, 2003
                                                 -------------------         -------------------
                                                                                    
GAAP Ratios
Losses and loss expenses ratio                                  53.4%                     54.9%
Acquisition expense ratio                                       20.6%                     18.2%
General and administrative expense ratio                         7.6%                     10.3%
                                                 -------------------         ------------------
   Combined ratio                                               81.6%                     83.4%
                                                 ===================         ==================



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                        ENDURANCE SPECIALTY HOLDINGS LTD.

                                 RECONCILIATION

            FOR THE QUARTERS ENDED MARCH 31, 2004 AND MARCH 31, 2003

       (in thousands of United States dollars, except per share amounts)

The following is a reconciliation of the Company's net income to operating
income and annualized operating return on average equity (both of which are
non-GAAP measures) for the three months ended March 31, 2004 and 2003:



                                                      Quarter Ended          Quarter Ended
                                                      March 31, 2004         March 31, 2003
                                                      --------------         --------------
                                                                          
Net Income                                              $   100,872             $    51,201
Add (Less) after-tax items:
   Net foreign exchange losses (gains)                        2,415                  (2,331)
   Net realized (gains) on investments                       (4,602)                 (4,001)
                                                        -----------             -----------
Operating Income                                        $    98,685             $    44,869
                                                        ===========             ===========

   Average equity [a]                                   $ 1,703,959             $ 1,343,024
                                                        -----------             -----------

Operating return on average equity                              5.8%                    3.3%
                                                        -----------             -----------
Annualized operating return on average equity                  23.2%                   13.4%
                                                        ===========             ===========


[a]   Average equity is calculated as the arithmetic average of the beginning
      and ending equity balances for the stated period.

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