Abstract <p>Algorithms for solving and calculation results for the problem of the movement of material in a rectangular pipe under the action of an increasing pressure drop in the frame of theory of finite elastic-viscoplastic strains are presented. The problem with specifying reversible and irreversible deformations by differential equations of their transfer is reduced to solving a system of differential equations with no-slip conditions on the pipe walls. An approximate solution of such a problem by the finite-difference method remains within the framework of the classical approach, without encountering additional difficulties. The elastic properties of an incompressible material are specified by a three-constant dependence of the elastic material on the invariants of the Almansi tensor, viscoplastic properties by flow theory with a generalized condition of maximum von Mises octahedral stresses for the case of taking into account the viscous resistance to plastic flow. The time and place of origin of viscoplastic flow, the patterns of movement of elastic-plastic boundaries, the elastic core, the evolution of stagnation zones in the corners of the pipe are calculated.</p>