Аннотация:From the formulated variational principles of Lagrange, Castigliano and Reissner type for the theory of multilayer thin bodies, the corresponding variational principles for the five-layer theory of thin bodies in the moments relative to systems of orthogonal polynomials under various interlayer contact conditions are derived. As special cases, classical and micropolar prismatic and cylindrical thin bodies are considered. The Lagrange principle is considered in more detail and on the basis of it, a finite element is created.