The effective method basing on theory of R-functions and variational structural method is developed for 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 non-linear deformation of shallow shells and plates with complex shapes in plane are established.
