A thin-walled tube subjected to internal and external pressure under the conditions of double-sided mechanochemical corrosion is considered. The rates of corrosion are supposed to be linearly dependent on the maximum principal stress. Previous solutions for thin cylindrical shells obtained by other authors reflect only the effect of differential pressure (i.e., the difference between internal and external pressure) and do not depend on the internal and external pressure values themselves. The model proposed here allows to take into account the effect of hydrostatic pressure on the durability of the tube exposed to corrosive environment, but it is not so cumbersome as the accurate solution for the double-sided corrosion of a pressurized tube based on the solution of Lamé problem for a thick-walled cylinder. The problem is reduced to an ordinary differential equation of the first order, which is solved in a closed form. It has been observed that the computational results for the classical thin shell model and for the proposed here refined model are very close to each other when either internal or external pressure is equal to zero. But the difference between the mentioned results grows as the minimum of the pressure values increases.