Most structural materials demonstrate very strong anisotropy in their properties. Due to this, during the elastic deformation of polycrystalline materials, there are very large differences between stresses loading of crystallites, which have different grain orientation. The consequence of the large differences in stress values is that at the beginning of the plastic deformation only some of the crystallites deform plastically. In different materials the anisotropy determines in which crystallites the plastic deformation will commence. This phenomenon is especially significant at the alternative loading; because of this some crystallites deform only elastically while others deform elastically and plastically as well. In these cases the failures (cracks) start in the last crystallites.