PRICING SUPPLEMENT NO. 29                                         Rule 424(b)(3)
DATED:   August 26, 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: $100,000,000   Floating Rate Notes [x]  Book Entry Notes [x]

Original Issue Date: 9/2/2004    Fixed Rate Notes [ ]     Certificated Notes [ ]

Maturity Date:  3/2/2006         CUSIP#: 073928G31

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 Date(s):

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:  Monthly

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

[x]  LIBOR Telerate

[ ]  Prime Rate

[ ]  CMT Rate

Initial Interest Rate: 1.65%             Interest Payment Period:  Monthly

Index Maturity:  One Month

Spread (plus or minus):  -0.02%

*  On the 2nd of each month prior to Maturity.
** On the 2nd of each month, includng the maturity date.

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