The issues of evaluation of the strength and durability of pipelines are relevant from an economic and environmental point of view, as well as to prevent man-made accidents. The article examines the stress state of the linear part of the pipeline, bent due to the given ground movements. The problem is solved within the framework of the linear theory of elasticity using the hypothesis of flat sections and taking into account the axial tension caused by the elongation of the pipe.The effect of thinning of the pipe wall due to general uniform corrosion on its stress state at fixed displacements and inclination angles of the end sections is also investigated. Some examples are presented to illustrate the uncertainty of the known solutions that do not take into account axial tension in the pipe, compared with the solution described in this paper.