The diffusion coefficients of acetone, methyl acetate, and chloroform in amorphous poly(vinyl acetate) are estimated using the solvent evaporation method. The evaporation process from polymer solutions, cast in the form of thin films, is studied as a numerical experiment. The process is modeled as a coupled heat and mass transfer problem with a moving boundary. Lattice fluid (LF) thermodynamics is used to describe polymer-solvent system volumetric properties and to derive appropriate expressions for solvents' chemical potentials. The resulting nonlinear system of governing equations is solved with the Galerkin finite element method. The estimated diffusion coefficients are in satisfactory agreement with reported data.