AbstractAs 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. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 1000–1013, 2001