The three-dimensional (3D) models of plates made of an anisotropic material are described by assuming the external load and harmonic functions of tangential coordinates. The problem on the strain of a plate is considered with free face planes and ignore the boundary conditions at the edges, and define the equations of equilibrium and the boundary conditions after the separation of the time-dependent multiplier. It is found that the normal stresses can be neglected and that the transversely tangential strains vary by the linear law with the plate thickness. The asymptotic solution of the set of equations is constructed with the assumption that the thickness of plates is small with respect to the wavelength without using the hypotheses about the distribution of displacements over the plate thickness.