A glazing fastener for mounting either rigid or flexible storm windows employs two elongated plastic strips: a channel strip having a narrow lengthwise channel, and a glazing strip having a narrow lengthwise insert flange for insertion into the channel. Walls of the channel and sides of the insert flanges have pairs of spaced apart longitudinal complementary ribs sized and positioned for interengagement. In a flexible glazing strip such ribs also enable the flexible plastic to be progressively stretched for a wrinkle-free fit. The glazing strip also has a laterally extending external flange positioned to remain outside the channel for engaging the glazing sheet, either to hold a rigid glazing sheet in place or to apply tension to a flexible glazing sheet. Various embodiments of the external flange are described including an embodiment adapted for use as an independent frame in a sliding window sash. The channel strip is oriented with respect to the window so that its channel cooperates with the shape of a selected insert flange to translate forces which would otherwise tend to separate the two strips, into a force which interlock the strips more tightly together. The channel strips are provided with means for attachment to a window frame, either a flat attachment surface or a sliding-type channel for removably mounting the fastener to a T-shaped flange on a window frame.