The present article is focused on a phenomenological description of a polymer workpiece Equal Channel Angular Extrusion (ECAE) through 2θ-dies of Segal and Iwahashi geometries with a channel intersection angle 2θ = 105° with fixed and movable external inlet and outlet die walls. The local flow dynamics, including the formation of macroscopic rotation and a dead zone appearance during the flow of plasticine, paraffin, and wax workpiece models through the subject die configuration was studied using physical simulation techniques. The present article utilizes a Computational Fluid Dynamics (CFD) numerical approach to a theoretical description of 2D viscous flow of incompressible Newtonian continuum through the stated die geometries. The boundary value problem for the Navier-Stokes equations in the curl transfer form for the local viscous flow was formulated and numerically solved with a finite-difference method. Theoretical CFD-derived plots with computational flow lines, dimensionless flow and curl functions, flow velocities, and tangential stresses for viscous material flow through the stated die geometries have been generated and described. As a first rheological approximation the derived computational results provide the theoretical description of physical simulation experiments and visualize the formation of ECAE-induced rotational modes of large deformations like macroscopic rotation and rotational inhomogeneity.