We have employed a pseudospin-phonon interaction model to investigate ferroelectric transitions in epitaxial ferroelectric films on substrates. Using the double-time Green's function method, we have calculated a pseudospin-phonon spectrum, effective pseudospin interaction constants and effective tunneling frequency. Numerical calculations give phase diagrams under various parameters. Without taking into account the pseudospin-phonon interaction in the interface, the Curie temperature at the surface, T-c, was lower than that for the bulk, T-b Taking into account the pseudospin-phonon interaction in the interface, T-c changed from the case of T-c > T-b to that of T-c < T-b with the layer number N 2, leading to a critical value of the effective tunneling frequency. Under different effective tunneling frequencies, phase diagrams were obtained for various layers of the films. T-c changed from the case of T-c < T-b to that of T-c > T-b as N greater than or equal to 2, leading to a critical effective pseudospin interaction in the interface. The lattice mismatch led to stresses in the interface between the film and substrate and led to changes in both the pseudospin-phonon interaction and tunneling frequencies, thus altering the phase transition temperature of films.