There were questions about the variation range of pressures and vessel size when the analytical solutions for the corrosion of an elastic thick-walled sphere under pressure in terms of the maximum principal stress can be applied. In the paper the conditions are presented under which the maximum (in absolute value) principal stress in the sphere both inside and outside is the circumferential one. Moreover, these conditions are satisfied for the entire corrosion process. These conditions must be met when applying the mentioned solution and/or the maximum normal stress criterion with respect to the hoop stress for a pressurized spherical vessel. The weakened conditions of the constancy of the sign of the circumferential stress are also given.