The present invention is directed to thermoplastic elastomer films and bags made from thermoplastic elastomer films and also to methods for making thermoplastic elastomer films and bags. The thermoplastic elastomer films of the present invention are composed of thermoplastic elastomers and non-elastic polyesters. The bags of the present invention are fabricated using blended monolayer thermoplastic films that include a blend of thermoplastic elastomer and a non-elastic polyester, or co-extruded multi-layer films that include at least one layer of thermoplastic elastomer and at least one layer of non-elastic polyester. The blended monolayer thermoplastic films of the present invention are useful in the food handling industry and particularly in the meat packaging industry and for use in cooking bag applications. The co-extruded films of the present invention are also useful in the food handling industry and particularly the meat packaging industry and for use in meat casing applications.