The stress-strain state of a thick-walled spherical shell is considered under the conditions of compressibility of the material and the nonlinear law of hardening. Using the equations of the relationship between stresses and deformations according to the method of variable elasticity parameters, an integral equation of compatibility of logarithmic deformations is obtained. When performing numerical calculations using the method of simple iterations, the moment of unstable deformation of the spherical shell is determined. The dependences of the relative pressure on the radial displacement of the points of the outer surface of the spherical shell are obtained, taking into account the compressibility of the material and without taking into account the compressibility for an ideal elastic-plastic material and for an elastic-plastic material with nonlinear hardening. According to the results of numerical calculation, failure to account for compressibility introduces a significant error in the calculation of radial displacements of the outer surface. The results of the study will allow us to determine the maximum permissible load of a thick-walled spherical shell corresponding to stable deformation.