The dry-cast membrane-formation process is a major phase-inversion technique by which asymmetric membranes are manufactured. In this paper a fully predictive model which incorporates coupled heat and mass transfer is developed to describe the evaporation of both solvent and nonsolvent from an initially homogeneous polymer/solvent/nonsolvent system. This unsteady-state, one-dimensional, coupled heat- and mass-transport model allows for local film shrinkage owing to excess volume of mixing effects as well as evaporative solvent and nonsolvent loss. The model can predict composition paths into the ternary phase diagram which determine the onset of phase transition. The ternary phase diagram is predicted using the Flory-Huggins theory allowing for composition-dependent interaction parameters. The model is applied to the well-characterized cellulose acetate/acetone/water system for which sufficient experimental data are available to permit determination of the friction coefficients in the ternary mass-transport model. The model is solved numerically using a software package based on the method of lines which is capable of handling moving boundary problems. The modeling studies indicate that for a given polymer/solvent/nonsolvent/support system, the most influential parameters are the gas-phase mass transport, initial cast film thickness, and initial composition. Of particular importance, the model can predict the general morphological characteristics associated with the formation of dense polymer films and symmetric as well as asymmetric membranes.