The paper concerns the problem of the double-sided mechanochemical corrosion of an elastic thick-walled sphere subjected to internal and external pressure. The corrosion rates on the inner and outer surfaces are assumed to be exponentially dependent on time and linearly dependent on the equivalent stress. Two analytical solutions are compared: one of them is developed by the use of the maximum principal stress and the second uses the von Mises stress for the equivalent stress. It is shown that the model using the maximum principal stress reflects the effect of hydrostatic pressure on the lifetime of the shell.