The manufacture of bulk parts from metastable powder materials requires new approaches to cold consolidation. One potential technique is equal-channel angular extrusion (ECAE), a simple shear process. This thesis describes an investigation into the effects of confining pressure (back-pressure) on single-pass, right-angled ECAE consolidation of copper and aluminum 6061 powders below 250°C, using an extrusion machine designed and constructed for this purpose. Empirical relationships for punch pressure requirements as a function of back-pressure and billet length are determined experimentally and compared with published theory. Powder particle boundaries are examined in extruded billets, revealing pores and regions of localized shear formed under low back-pressure conditions. This shear localization is considered with a visualization experiment involving wax spheres in a transparent die, and a linear stability analysis of simple shear of a thin strip of material described by a generalized powder yield function and flow rule. The back-pressures required to obtain homogeneous, pore-free microstructures are determined, and related to the response of the powders during the initial compaction stage of ECAE. Interparticle bond formation in cold powder processing is briefly discussed in the context of multi-pass extrusions.