The present article is focused on a 2D computational fluid mechanics study of local viscous flow dynamics and the formation character of rotary modes of deformation during Equal Channel Multiple Angular Extrusion (ECMAE) of a polymer workpiece fluid model through a U-shaped die with parallel slants in channel intersection zones. The present local flow problem was experimentally analyzed using physical simulation methods and theoretically studied with numerical fluid mechanics techniques. The computational approach has been grounded on the numerical finite difference solution of the boundary value problem for the Navier-Stokes equations in the curl transfer form for the local viscous flow of incompressible Newtonian fluid through a U-shaped rectangular die with parallel slants. The derived research results allow us to draw a conclusion that the implementation of a geometric design of parallel slants within a 2-turn U-shaped die results in localization of the maximum tangential stresses within the workpiece volume to the vicinity of these parallel slants during ECMAE.