Two approaches to constructing the equations of a layered medium are considered. The first approach uses cinematic hypotheses of the distribution of displacements (transverse and normal) over the thickness of anisotropic layers. The hypotheses make it possible to account for transverse shear and compression of the layers. In the second approach, modified equations of the elastic layer are used. These equations were constructed by approximating stresses and displacements with Legendre polynomials. The order of the system of differential equations of elastic layer in this case does not depend on whether the stresses on the front surface of the layer or displacements are specified. This allows constructing a system of differential equations of a layered medium using the displacement coupling conditions and stresses on the contact surfaces.
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