Photographic films are multilayer polymer structures coated from solution onto a relatively rigid substrate, chilled into a solid gel, and then dried into a permanent coating. This model predicts stress growth and defect formation during drying of such films that remain above their glass transition temperature, so that Fickian difision persists. The stress in the drying gel is taken from mixture theory; the polymer network is a nonlinear elastic or hypoelastic solid, whereas the solvent is an ideal fluid. Conservation laws and constitutive equations are formulated in terms of the polymer network velocity and discretized by the mixed method of Guenette and Fortin on an elliptically genereted, independently evolving finite-element mesh. Results include evolution of polymer velocity, free surfaces, solvent concentration, and residual stress. Various model problems are solved for drying of uniformly coated films, suspended films (as in tenter-frame ovens) and around rigid particle inclusions in suspended films and in multilayer photographic coatings causing particle migration and drying defects.