Novel thermoplastic sheet materials for permitting positionable and repeated repositionable use of tape fasteners therewith without experiencing substnatial loss of tape adhesion therebetween are disclosed. A novel thermoplastic sheet material generally comprises an ethylene polymer and an anti-popoff polymer in an effective amount for increasing and substantially maintaining the tape adhesion. The increase in and substantial maintenance of the tape adhesion is accomplished without adversely affecting the properties or cost of the thermoplastic sheet material. A preferred formulation for producing the novel thermoplastic sheet material comprises polyethylene as the ethylene polymer and a polypropylene or alpha-methyl styrene as the anti-popoff polymer. The novel thermoplastic sheet materials are especially suitable for use as films which can be used as backsheets in absorbent articles, such as, disposable diapers, bandages, surgical dressings or drapes and catamenial pads.