The effective method basing on theory of R-functions and variational structural method is developedfor solving
non-linear boundary problems. Elastic-plastic bending of thin shallow shells is considered. The problems are
reduced to finding stationary points of suggested mixed variational functionals according to the initial
linearization due to usage of subsequent loading and Newton-Kantorovich jointly with method of varying
elastic parameters. The method is used for automatic calculations in «POLE» programming system for
investigations of shell structural elements. The numerical justification of the method is given. New laws of nonlinear
deformation of shallow shells and plates with complex shapes in plane are established.
