disposable polymeric container covers , methods of manufacturing the same , and machines for manufacturing the same are disclosed wherein the cover may include a polymer film adapted to enclose a bowl or the like , and an elastic film proximate thereto adapted to seal the cover against the bowl . the elastic film may be provided as an annular member completely surrounding the bowl , or in segments around an otherwise non - elastic ring . the method may include co - extruding the elastic with the non - elastic polymer , or stamping the elastic and non - elastic polymers as separate pieces and then heat sealing them together .