

<PAGE>

                                                                    Exhibit 23.1

                         INDEPENDENT AUDITORS' CONSENT

We consent to the incorporation by reference in this Registration Statement of
Applied Extrusion Technologies, Inc. on Form S-8 of our report dated November
25, 1998 (December 16, 1998 as to Note 5), which expresses an unqualified
opinion and includes an explanatory paragraph relating to the adoption in 1998
of Statement of Position No. 98-5, "Reporting for the Costs of Start-Up
Activities," appearing in the Annual Report on Form 10-K/A of Applied Extrusion
Technologies, Inc. for the year ended September 30, 1998.


/s/ DELOITTE & TOUCHE LLP
-------------------------
DELOITTE & TOUCHE LLP
Boston, Massachusetts
May 10, 1999


