The process of production of capillary pipes, including drawing on a long movable mandrel and their subsequent running-in along the outer diameter in order to extract the mandrel to obtain finished pipes of the required quality, is considered. The FEM modeling is considered in two stages with a wide variation of the defining parameters with the compression of the pipe and its gap with the mandrel. At the first stage, the permissible compression was determined with a limit on the tolerance for the outer diameter. At the second stage, the occurrence of pipe facet was studied.