A film that contains a thermoplastic composition having a substantial portion of a renewable, natural starch polymer, and yet is elastic and exhibits good strength properties, is provided. Although starch is normally chemically incompatible with most elastomeric polymers due to their different polarities, the present inventors have discovered that phase separation may be minimized by selectively controlling certain aspects of the film, such as the nature of the elastomeric polymer and the starch polymer, and other film components, the relative amount of the film components, and the process for making the film.