The present work is focused on a 2D fluid dynamics description of equal channel multiple angular extrusion (ECMAE) or equal channel multiple angular pressing (ECMAP), using a numerical mathematical simulation for viscous flows of physical polymeric materials models through a die with a movable inlet wall. A numerical finite-difference model for plane viscous Newtonian flow of an incompressible continuous medium in a multiple-angle region with a movable inlet die wall, based on the formulation and numerical solution of the boundary value problem for the Navier-Stokes equations in curl transfer form, is derived. A numerical estimation of the influence of the direction of movement of a movable entrance die wall on computational flow lines, stream and curl functions, and viscous flow velocity fields was carried out within the scope of the developed model for a movable inlet wall of the die. The proposed hydrodynamic approach extends the ideas concerning the dynamics of the macroscopic rotation formation within the volume of the viscous physical model of a polymeric material during ECMAE or ECMAP through a die with a movable inlet wall.