Simple unified analytical solution is presented for the lifetime of cylindrical, spherical, and toroidal vessels subjected to one- or double-sided mechanochemical corrosion under internal and external pressure. This solution provides sufficiently accurate results for perfect cylindrical and spherical vessels, while for toroidal vessels it gives approximate estimates based on the weakest cross-section principle. The obtained solution reflects the difference in the hoop stresses at the inner and outer surfaces of the vessels and the effect of hydrostatic pressure (i.e. minimum of the internal and external pressures) on the vessel lifetime. It is shown that high hydrostatic pressure may noticeably reduce the durability of the vessels or, on the contrary, slightly increase it. The need for an integrated approach – using different methods – to solving such problems is emphasized.