PRICING SUPPLEMENT NO. 31A                                        Rule 424(b)(3)
DATED:  September 1, 2004+                                   File No. 333-109793
        October 27, 2004++
(To Prospectus dated November 17, 2003,
and Prospectus Supplement dated November 17, 2003)

                                 $10,668,950,162
                         THE BEAR STEARNS COMPANIES INC.
                           Medium-Term Notes, Series B

Principal Amount:  $450,000,000  Floating Rate Notes [x]  Book Entry Notes [x]

Original Issue Date:  9/9/2004^  Fixed Rate Notes [ ]     Certificated Notes [ ]
                     11/1/2004^^

Initial Public Offering Price:  100%>
                                100.033%>>

Maturity Date:  9/9/2009        CUSIP#: 073928G56

                                Euroclear and Clearstream Common Code: 020066784

Option to Extend Maturity:      No    [x]
                                Yes   [ ]   Final Maturity Date:

                                Optional Optional

                         Redemption           Repayment           Repayment
   Redeemable On          Price(s)             Date(s)            Price(s)
   -------------       --------------       -------------        -----------

        N/A                  N/A                 N/A                 N/A

Applicable Only to Fixed Rate Notes:
-----------------------------------

Interest Rate:

Interest Payment Dates:

Applicable Only to Floating Rate Notes:
--------------------------------------

Interest Rate Basis:                     Maximum Interest Rate:  N/A

[ ]   Commercial Paper Rate              Minimum Interest Rate:  N/A

[ ]   Federal Funds Effective Rate

[ ]   Federal Funds Open Rate            Interest Reset Date(s):  *

[ ]   Treasury Rate                      Interest Reset Period:  Quarterly

[ ]   LIBOR Reuters                      Interest Payment Date(s):  **

[x]   LIBOR Telerate

[ ]   Prime Rate

[ ]   CMT Rate

Initial Interest Rate: 2.13%             Interest Payment Period:  Quarterly

Index Maturity:  Three Months

Spread (plus or minus):  +0.27%


+     $400,000,000 was traded on September 1, 2004.

++    $50,000,000 was traded on October 27, 2004.

^     $400,000,000 was issued on September 9, 2004.

^^    $50,000,000 was issued on November 1, 2004. These Notes will have interest
      accrued from September 9, 2004 for the Interest Payment Date on December
      9, 2004.

>     The Notes issued on September 9, 2004 had an Initial Public Offering Price
      of 100%.

>>    The Notes issued on November 1, 2004 had an Initial Public Offering Price
      of 100.033%.

*     On the 9th of each December, March, June and September prior to Maturity.

**    On the 9th of each December, March, June and September, including the
      maturity date.

                  CERTAIN US FEDERAL INCOME TAX CONSIDERATIONS

            The following discussion supplements the section captioned "Certain
US Federal Income Tax Considerations" in the Prospectus Supplement dated
November 17, 2003.

Qualified Reopening

      We will treat the Notes issued on November 1, 2004 as part of the same
issue as the Notes issued on September 9, 2004 (the "Original Notes") for US
federal income tax purposes. Accordingly, for purposes of the Treasury
regulations governing original issue discount on debt instruments (the "OID
Regulations"), we will treat the Notes issued on November 1, 2004 as having the
same issue date, the same issue price and, with respect to holders, the same
adjusted issue price as the Original Notes. Consequently, the "issue price" of
the Notes issued on November 1, 2004 for US federal income tax purposes will be
the first price at which a substantial amount of the Original Notes were sold to
the public (excluding sales to bond houses, brokers, or similar persons or
organizations acting in the capacity of underwriters, placement agents, or
wholesalers). The purchase price for the Notes issued on November 1, 2004 will
reflect interest accrued from September 9, 2004 ("pre-issuance accrued
interest"), which will be included in accrued interest to be paid on December 9,
2004. In accordance with the OID Regulations, we will exclude pre-issuance
accrued interest from the issue price of the Notes issued on November 1, 2004.
Accordingly, US Holders of the Notes issued on November 1, 2004 should treat a
corresponding portion of the interest payable on December 9, 2004 as a return of
the excluded pre-issuance accrued interest, rather than as an amount payable on
the Notes issued on November 1, 2004.

The distribution of Notes will conform to the requirements set forth in Rule
2720 of the NASD Conduct Rules.

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