The problem of calculating bending plates by the finite element method with considering of shear deformations is considered. The bending plates are widely used as common structures of various objects of civil and industrial construction. The solution was obtained on the basis of the principles of the minimum of additional energy and possible displacements. For approximation of moment fields, piecewise constant functions are used. Shear forces can be approximated by constant or piecewise constant functions. The necessary relations for rectangular and triangular finite elements are obtained. It is shown that the proposed method can be used in combination with traditional finite elements for thin plates obtained by the finite element method in displacements. A comparison of the solutions, obtained by the proposed method, with other known solutions for bending plates, with assuming of shear deformations, is given. A numerical estimate of the accuracy and convergence of the proposed method, when crushing the finite element mesh, is given.