We investigate the drying phenomenon in polymer coatings by developing a model that accounts for the polymer-lean phase (liquid) and the polymer-rich phase (solid), while predicting the stress in the coating. The governing equations are developed for the two phases separately. In the dilute polymer region, the effect of polymer diffusion on its concentration distribution is considered. The polymer-rich phase is modeled as a porous structure, with entangled polymer chains whose diffusive motion is arrested. We employ Biot's theory to model the porous skin and to determine the stress in the coating. The governing equations are solved by employing a finite difference scheme. The effects of polymer diffusion and the skin's permeability on the coating stress are studied. We find good agreement between the predictions of the polymer concentration profile and that obtained from measurements.