The Channel Angular Extrusion (CAE) technique is a process, in which a deformable solid material is led to yielding through the intersection of inclined channels. Compared to classic plastic deformation, the process is technically simple but the material experiences, instantly, large plastic deformation. The deformation occurs locally and high internal stresses develop during the process. In most cases the process is used for grain size refinement. Equal Channel Angular Extrusion (ECAE) is a special case where the intersecting channels are of equal cross sections. In this paper, an analytical study of the internal stresses and those developed along CAE tools is presented. A deformation model is introduced for the general process of channel extrusion in which the intersecting channels are not necessarily equal. The procedure splits the material at the intersection of the channels into two zones; one causes the deformation while the other remains rigid. The analysis is also applied to the particular case of ECAE, and the results are compared with those obtained from a finite element analysis and the overall experimental pressure.