RICING SUPPLEMENT NO. 41                                          Rule 424(b)(3)
DATED: May 4, 2001                                            File No. 333-52902
(To Prospectus dated January 11, 2001,
and Prospectus Supplement dated January 11, 2001)

                                 $9,015,893,162
                         THE BEAR STEARNS COMPANIES INC.
                           MEDIUM-TERM NOTES, SERIES B

Principal Amount:  $50,000,000  Floating Rate Notes [x] Book Entry Notes [x]

Original Issue Date:  5/8/2001  Fixed Rate Notes [  ]   Certificated Notes [  ]

Maturity Date:  5/8/2002        CUSIP#: 073928TY9

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

[ x ]    Federal Funds Rate            Interest Reset Date(s):  Daily

[  ]     Treasury Rate                 Interest Reset Period:  Daily

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

[  ]     LIBOR Telerate

[  ]     Prime Rate

[  ]     CMT Rate

Initial Interest Rate:  4.6375%        Interest Payment Period: Quarterly

Index Maturity:  N/A

Spread (plus or minus):  + 0.20%

* On the 8th of August, November, February and at Maturity.

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