The recent successful development of the equal channel angular pressing (ECAP) process in metals provides a feasible solution to produce ultra-fine or nano-grained bulk: materials with tailored material properties. However, ECAP is difficult to scale up commercially due to excessive load requirements. In this paper, a new Multi-ECAP process with die rotation is considered to obtain ultra-fine grain structured materials under a moderate deformation force. It is shown that an addition of torsion results in a reduction in the pressing force and an increase in severity of plastic deformation. An analysis using the upper bound method is found to be useful in predicting the pressing load and flow pattern of ECAP with and without rotational dies. Solutions are obtained for different inclined channel angles under different angular velocities of dies. Relative pressures are presented and some computed solutions are compared with those found by FEM simulation. The theoretical predictions of the pressing load are in good agreement with the simulation results. The amount of plastic deformation is determined by the inclined angle between the two intersecting channels, and the velocity ratio between the angular velocity of dies and the normal component of the punch velocity.