This is a freewheeling resilient rotary diecutting anvil cover comprising a flexible member of one or multiple pieces releasably secured together along a generally axial line or lines including one or more annular ribs on the inner surface for disposition in annular grooves in the cylindrical supporting base in which at least the portions of the rib or ribs leading to the releasable connection or connections are of split T-cross section and collapsible to relieve binding and to permit installation and removal from a head, or the like, without removing the head. In a modification, a cover lengthened by use can be cut to smaller size. Another modification employs a metal plate or plates to reduce lengthening.