A coextruded, heat shrinkable, thermoplastic multilayer film for packaging fresh red meat cuts and processed meats. The film comprises a first layer comprising very low density polyethylene, a first core layer of vinylidene chloride-methyl acrylate copolymer, and a second layer comprising very low density polyethylene. In another embodiment the first layer is a second core layer confined between said first core layer and a first outer layer comprising a heat sealable thermoplastic polymer or copolymer. In a further embodiment the second layer is a second core layer confined between said first core layer and a second outer layer comprising a thermoplastic polymer or copolymer.