This work is devoted to constructing a modified non-classical theory of plates
without preliminary hypotheses about the distribution of the displacement vector and the deformation
tensor on the basis of three-dimensional equations of the nonlinear elasticity theory of
V.V.Novozhilov The proposed approach is applicable to deformation of non-canonical plates and
shallow shells. The recurrent relations have been obtained; they will be further used in determining the
ratios of interlayer variables in layered composites.