The problems of the general corrosion of pressure vessels have been investigated by a number of scientists using the law of P.-S. Laplace for thin shells. However, the existing solutions based on Laplace's law provide satisfactory prediction of the vessel's lifetime only for corrosion independent of stress and for mechanochemical corrosion when the values of the internal and external pressure are not high or do not greatly exceed their difference. In this regard, a new, refined analytical solution for the mechanochemical corrosion of a thin-walled spherical shell is presented that is valid for any combination of pressures. The new solution does not have the limitations inherent in the existing solutions for thin shells, such as the neglect of the change in the circumferential stress through the shell thickness and the effect of the total component of the internal and external pressure (hydrostatic pressure). At the same time, the new solution has the same simple form as the existing solution based on Laplace's law, with only one constant being different; therefore, the accuracy of existing algorithms based on Laplace's law can be improved significantly for high pressures only by replacing certain constants. The conditions of the applicability of the hoop stress in a thin sphere as an effective stress in strength criteria and corrosion kinetics models are specified. Formulae for the prediction of the lifetime are obtained in terms of both wall thickness and maximum stress. An algorithm of comparative strength and stability analysis is presented which, unlike the recent solution, takes into account that the critical state should be formulated for the unknown in advance thickness of the corroded vessel. Possible inhibition of corrosion is also taken into account. The conditions for cessation of the corrosion process before any limiting stress is reached are formulated. The influence of various initial data on the lifetime of the shell, as well as on the accuracy of the solutions, is analysed. It is shown that the same approach is reasonable to be applied to the problems of corrosion described by different corrosion kinetics models.