The paper concerns 2D problem of an elastic thick-walled pipe with an initial thickness variation, subjected to internal pressure and mechanochemical corrosion. The inner perimeter of the pipe cross-section is elliptical, while the outer is circular. The linear Dolinskii corrosion kinetics model is used. In the general case, structural instability of initial boundary value problems with unknown evolving boundaries can cause the divergence of numerical procedures when modelling the processes under study. It is observed that the attempts to circumvent the divergence of numerical procedure can suppress the manifestation of mechanochemical effect and yield inaccurate results. Thus, it is necessary to find a compromise between competing computational processes. Calculations revealed that the variation of the initial pipe wall thickness within the acceptable pipe wall tolerance can noticeably accelerate the growth of stresses and, consequently, reduce the durability of the pipe. The applicability of analytical solutions for a perfect circular pipe with a reduced thickness, equal to the minimum thickness of the imperfect pipe, to the case under study is also discussed.