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In this paper we present the application of an anisotropic phase-field crystal model to the process of the heteroepitaxial growth in anisotropic systems. During the growth of the thin films with sheared non-cubic lattice the elastic strain gives rise to dislocations and grain boundaries due to the difference between the film and the substrate lattice in terms of lattice constant (misfit) and lattice shearing (anisotropy difference). The numerical simulations for various misfits and anisotropy difference demonstrate that the anisotropic evolution equation for the phase-field variables allows to simulate the growth of the layers in anisotropic systems. We investigate this phenomenon and derive the relationships for the phenomenological dependencies such as the dependence of the characteristic layer thickness and the number of defects on the misfit for various anisotropy difference based on our recently developed anisotropic phase-field crystal model.