The article is devoted to numerical study of convergence of calculation results obtained on the basis of two nonlinear models of the theory of shells with thickness decrease. As models are considered nonlinear theory of thin shells, based on the hypotheses of the Kirchhoff-Chernykh and hypotheses type Tymoshenko, modified K.F. Chernykh for the case of hyperelastic rubber-like material. As an example, we consider the problem of axisymmetric conical compression and spherical shell by axial force. The convergence of results with decreasing thickness is disturbed in areas stability loss(buckling). Also happens when in the deformation process is violated the basic assumption of the theory of shells - the thickness is much smaller than radius of curvature (h <<R).