The paper considers numerical solution for the problem of quasi-static axisymmetric eversion of a spherical shell (hemisphere) under action of external pressure. Results based on the general nonlinear theory of shells made of elastomers proposed by K. F. Chernykh. It is used two models of shells based on the hypotheses of the Kirchhoff and Timoshenko modified K.F. Chernykh for the case of hyperelastic rubber-like material. The article presents diagrams of equilibrium states of eversion hemispheres for both models as well as the shape of the shell at different points in the diagram.