Abstract: The present invention is a method for manufacture of elastic leg and/or waist disposable diapers. A preferred form of the diaper uses for the entire moisture impermeable backing sheet an elastomeric material of the type that is heat unstable and relatively inelastic in its unshrunk form and stable and relatively elastic in its heat shrunk form. Numerous materials of this type are available. Included among them are block copolymers which include a rubbery material as one component, polyurethanes, and irradiated polyethylene. Alternatively, a conventional polyolefin backing sheet may be used with strips of the heat shrinkable elastomeric material bonded in appropriate marginal locations in the waist or leg zones. These marginal zones are then heated to an appropriate temperature and any tension on the sheet relaxed to allow shrinkage and elasticization to take place.