The aim of this work was to develop a model to describe some microscopic phenomena in the epitaxial thin films based on lead zirconate PbZrO3. The model takes into account the epitaxial contact of the film with the substrate and conditions for mechanical compatibility of the domains. It includes contributions from pseudopolarization, elastic and domain-domain interactions as well as a contribution analogous to electrostriction in ferroelectric materials. The parameter optimization has been performed through free energy minimization with varying the magnitudes of elastic displacements and the pseudopolarization vectors. The results obtained qualitatively reproduced a part of the experimental observations on the domain matching in the thin films, to be exact, the change in microscopic twisting in the domain wall regions when removing the epitaxial structure away from the substrate.