Background The shifting of the key work scope of main pipeline construction to the regions with permafrost and difficult climate conditions because of the dislocation of oil and gas extraction centers to the new regions is the characteristic of pipeline transportation development in Russia in recent years. According to analysts, the reclamation of hydrocarbon fields in the areas with the permafrost soils in arctic and subarctic regions is going to carry forward in the coming years; in such areas the above-ground pipelines on supports are the optimal structural design [1]. However, as of today, the real conditions of working of linearly extended above-ground pipelines at permafrost are not sufficiently studied [2]. This article is concerned with one of the valid scientific objectives of this field - the study of the stress-strain state of above-ground pipelines at different friction coefficients at supports. Aims and Objectives The main purposes of the article are the study of the friction force’s influence at supports on the stress-strain state of linearly extended above-ground pipelines with trapezium-shaped compensation parts and the definition of the most optimal structural design that could minimize stress-strain state under construction at permafrost. Methods In compliance with the object and purpose, the following methods were used: analysis, comparison, generalization, and mathematical simulation (finite element analysis). Results The dependencies of pipeline’s peak transversal displacements (in horizontal plane) and stresses appearing in the deformation’s self-compensation process (in working state) on system’s design factors at different friction coefficients at supports (for various sliding friction pairs) were obtained as a result of the study of stress-strain state of an above-ground pipeline with trapezium-shaped compensator with the application of mathematical simulation.