PRICING SUPPLEMENT NO. 37                                         Rule 424(b)(3)
DATED:    October 13, 2004                                   File No. 333-109793
(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: $118,000,000   Floating Rate Notes [x]  Book Entry Notes [x]

Original Issue Date: 10/28/2004  Fixed Rate Notes [  ]    Certificated Notes [ ]

Maturity Date:  10/28/2014       CUSIP#: 073928H22

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:  7.00%

[  ]    Commercial Paper Rate                Minimum Interest Rate:  0.72%

[  ]    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: 2.83938%              Interest Payment Period:  Quarterly

Index Maturity:  Three Months

Spread (plus or minus):  +0.72%

* On the 28th of each January, April, July and October prior to Maturity.

** On the 28th of each January, April, July and October, including the maturity
date.

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