A fitted mattress cover for enveloping the top, side and end surfaces of a mattress is constructed to accommodate a range of mattress peripheral sizes and thicknesses. The construction utilizes composite end panels which include stretch end panels covering lower partial portions of the mattress end surfaces and which impart recovery forces to effectively grip the mattress and thereby minimize the shifting of the cover relative to the mattress. At the same time, the look and feel of the mattress covering, which may be of importance especially in the case of a fitted sheet, is improved, by virtue of the fact that the side panels can be formed as uninterrupted unitary extensions of the material forming the top side panel, or other material based upon aesthetic considerations, as can upper partial portions (extension end panels) of the composite end panels. In a related aspect, stretchability of the mattress cover skirt may be imparted in a post-manufacture heat treatment finishing step, which may included a laundry wash and dry cycle.