Static problems of the bending theory for plates and envelopes from composition materials are considered in the paper aiming at the possibility investigation of the more rational account of the cross shift deformation in plates and envelopes from composition materials, the development and application of the Green's function construction method to the normal deflection of orthotropic plates of variable thickness. As a result the method for the separate solution of teh source problem has been developed as well as the method of the Green's function construction for the normal deflection of plates of variable thickness. Green's functions for three classes of plates of variable thickness have been constructed. Boundary-value problems for plates and envelopes of constant thickness have been solved by the separation method developedAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio