As a solvent-cast polymeric coating dries, each part reaches a concentration at which it solidifies and develops elastic modulus. Thereafter, as further solvent departs, that part shrinks out-of-plane, but not in-plane, if the coating adheres to its: substrate. Hence, it develops in-plane elastic stress. If the stress grows large enough, the stress-free state may yield, which reduces the final stress level. A theoretical model of diffusion and mass transfer, large shrinkage-induced deformation, and elastic stress, together with yielding and postyielding viscous deformation, was developed to predict stress evolution in one-dimensional drying of polymer coatings. Concentration varies only perpendicularly to the substrate, the coating shrinks only in that direction, and the stress varies only in that direction but is in-plane isotropic. The predictions are compared with measurements of evolving stress in various solvent-cast polymer coatings and aqueous gelatin coatings by a cantilever-deflection method.