The paper concerns mathematical modelling of the general corrosion of elastic tubes and their optimal design, based on empirical corrosion kinetics equations and strength analysis. When the rates of corrosion of pipe surfaces are given functions of time, the problems of wear can be solved by conventional methods of computational mechanics. In the case of stress-assisted chemical reactions, we have initial boundary value problems with unknown variable boundaries and the instantaneous corrosion rates are unknown as well. Herein, analytical solutions are presented for the double-sided mechanochemical (and pure) corrosion of a tube under internal and external pressure when the equivalent stresses on its inner and outer surfaces are different, being defined by the solution of the Lame problem for a pressurised tube. Formulas for one-sided corrosion are included as well. The purpose of optimal design is to find an initial thickness of the pipe wall which provides a specified service life of the pipe and a minimum material consumption; the pipe capacity, internal and external pressure being given. For the decelerated corrosion process, the aim is also formulated as to determine a minimum initial thickness of the pipe such that corrosion has time to stop (due to inhibition) before a critical state is reached. Being based on the analytical solutions, the proposed methodology of optimal design does not require complex numerical procedures.