The objective of this article is the description of advantages of a slanted die geometry, used for equal channel angular extrusion (ECAE) of materials. The prime novelty statement of the present research is an experimental flow pattern, obtained with circular gridlines and a numerical solution of a viscous flow 2D problem for the slanted die, derived with Navier–Stokes equations in curl transfer form. The geometry of the slanted die was chosen for the case of a rectangular die with channel intersection angle 2 θ =  90° and with parallel slants in the channel intersection zone, where the slant width is equal to the inlet and outlet channel widths. Computational material flow kinematics, macroscopic rotation patterns, material flow velocity fields, tangential stresses, and punching pressure fields during viscous materials ECAE have been derived with a numerical finite-difference solution of the curl transfer equation for 2D viscous flow of incompressible continuum during ECAE. Theoretical results have been verified with physical simulation experiments by the introduction of initial circular gridlines. Both theoretical and computational results confirm the suitability and technological advantages of dies with parallel slants over the known Segal and Iwahashi dies for ECAE, as slanted convergent dies enable the reduction of the dead zone size and provide the minimization of dangerous macroscopic rotation during ECAE processing of both metal and polymer materials.