We have used a records destruction company for this purpose.  There are likely companies in your area.  They have trucks that actually do the shredding right there on site - it is amazing, actually.
The National Association for Information Destruction (NAID) is the standards body that governs this industry: http://www.naidonline.org/
You can probably find a qualified shredder near you from there.
Good luck!

Eleanor I. Cook
Assistant Director for Collections & Technical Services
Academic Library Services -- Joyner Library
East Carolina University
East Fifth Street
Greenville, NC 27858
252-328-2598
252-328-4834 fax
cooke@ecu.edu

-----Original Message-----
From: SERIALST: Serials in Libraries Discussion Forum [mailto:SERIALST@LIST.UVM.EDU] On Behalf Of Barbara Weir
Sent: Friday, March 02, 2012 11:11 AM
To: SERIALST@LIST.UVM.EDU
Subject: [SERIALST] Recycling bound JSTOR volumes?

We're looking for a recycling company that can dispose of our unwanted,
bound JSTOR print volumes.   Does anyone have suggestions for companies
in the Philadelphia area (or even farther away) which might be able to
do the job?  We prefer not to just throw these in the dumpster, but
haven't had much luck so far finding a company to take these away.

Thanks for any ideas you have.

Barb Weir

--
Barbara Weir
Associate Librarian for Technical Services and
     Digital Initiatives
McCabe Library
Swarthmore College
500 College Ave.
Swarthmore, PA  19081
610-328-8443
610-328-7329 (Fax)