
<PAGE>   1
                                                                    Exhibit 23.1


INDEPENDENT AUDITORS' CONSENT

We consent to the incorporation by reference in Registration Statement Nos.
33-44449, 33-48841, 33-64656 and 33-80804 of Applied Extrusion Technologies,
Inc. On Form S-8 of our report dated November 14, 1996, appearing in this Annual
Report on Form 10-K of Applied Extrusion Technologies, Inc. for the year ended
September 30, 1996.

/s/ Deloitte and Touche LLP
---------------------------

Boston, Massachusetts
December 12, 1996

