Mine subsidence can pose a considerable threat to pipeline integrity. There are three constituents which quantitatively determine the distribution of strains along the pipelinethe function of ground displacement along the pipeline axis; the physical law of soil-pipe interaction due to their relative displacements; and the pipe wall deformation response to axial stress. All three of them are usually well understood but there are still a small number of successful examples of prediction of stresses in such pipelines due to lack of effective algorithms of their accounting for. So here we develop the effective procedure for axial strain and displacement calculation based on notions of basic and correction solutions. The basic solution is algebraically corrected after each iteration step for correction solution, which obtained by numerically efficient transfer matrix method. The role of basic one is very narrow here: first it determines the particular type of law of soil-pipe interaction; second, the resulting solution is considered to be correct when basic and correction solutions coincide. The effectiveness of the algorithm application is shown on number of real examples.