As a coating solidifies by drying, it tends to shrink. It is liquid enough in early stages that any shrinkage stress is rapidly relieved by viscous flow. It becomes solid enough in later stages to support elastic stress, which results from shrinkage inhibited by adherence to the substrate. Stress can relax by viscous creep in the coating. Thus, the stress level is an outcome of competing shrinkage and relaxation. A theoretical model of diffusion and mass transfer, large shrinkage-induced deformation and stress, together with yielding and post-yielding viscous deformation, was developed to predict stress evolution in drying of polymer coatings after solidification. The coupled equations of diffusion and stress development are solved by the Galerkin/finite-element method. This model is used in polymer coatings to study the effect of a grooved substrate and embedded particles to the stress and drying, and to simulate cantilever deflection method used to measure stress experimentally.