(Letterhead of Cahill Gordon & Reindel)











                        January 23, 1997



                                                  (212) 701-3000


          Re:  Prudential Unit Trusts
               Insured Tax Exempt Series 31
               (Registration No. 33-17354)


Dear Sirs:

          On behalf of Prudential Securities Incorporated, 
pursuant to Rule 477 of the Securities Act of 1933, we hereby
request the withdrawal of the registration statement filed for the
above-captioned Trust on December 19, 1996, CIK number 0000822705,
accession number 0000898733-96-001093.  Such filing was transmitted
on Edgar on Form Type 485BPOS. Inadvertenaly, such filing contained
inaccurate CIK and CCC codes ( a corrected filing with the correct
codes was transmitted on December 23, 1996.

          Please do not hesitate to call the undersigned, collect,
at (212) 701-3484, with any questions.  

                                        Very truly yours,

                                        Philip A. Heimowitz
                                        Philip A. Heimowitz
     
Securities and Exchange Commission
450 Fifth Street, N.W.
Washington, D.C. 20549