The paper describes the setting of the problem for determining of the bearing capacity and the supercritical behavior of thin-walled and combined axisymmetrical bodies, taking into account geometric nonlinearity. Submersible vehicles of various purposes and their constructive elements are typical examples of such an object. These include rescue devices, refueling cylinders, manhole covers with supportive massive thick-walled layers. The structural features of these objects are the need to combine within the meridional cross section of spherical, cylindrical and toroidal elements with different ratios of wall thickness and radius of the median surface of the shell. Significant influence on the calculation results of some bearing elements such as manhole covers with massive reinforcing layers and elastic support linings leads to the need to consider within the framework of one calculation scheme of axisymmetric bodies of complex structure, which include a combination of massive and thin-walled components. This requires creation of a corresponding finite elements library. Definition of critical pressure values at which plastic deformation arises or bearing capacity loss is realized can not be fulfilled on the basis of the theory of thin shells of a canonical form and requires the development of calculating methods for composite shells of medium thickness. Their calculations can not be limited by a linear elastic setting and need information about the level of development of irreversible deformations and the influence of geometric nonlinearity on the of critical load value. The correlation between the theory of plastic flow and the nonlinear theory of elasticity is taken as the output. The connection between stresses and deformations is taken within the framework of the theory of plastic flow. Relationships between deformations and displacements regarding geometrical nonlinearity are formulated.