Drying kinetics of a polymer film cast from a polymer-solvent solution is studied. A modelization of the whole drying process is performed including the diffusion of solvent through the varnish layer, the moving interface, and the coupled heat and mass transfer between the interface and the drying air. The assumptions and the validity domain of the proposed modelization are thoroughly analyzed. In particular comparison of the varnish temperature with its glass transition temperature all along the process allows us to determine the validity domain of the Fickian diffusion assumption. Because of the hypodiffusive behavior of polymer solutions, very large concentration gradient appear in the layer, and the drying kinetics ir characterized by two successive regimes. This two-stage kinetics is investigated first for typical conditions encountered in the packaging industry, where a film of a few microns is dried in a few seconds, thanks to hot air blown through nozzles. Then, different drying conditions corresponding to evaporation experiments at room temperature of thicker films of the same varnish are studied.