The mechanical response of frictional powders under quasi-static loading is studied by means of two- and three-dimensional discrete element methods, compared directly with each other. The response of the system is characterized by elastic behavior for very small deformations, softening, plastic yield and critical state flow at large strain. The maximal yield stress is reached for some finite deformation of a few percent, but the decay to the critical steady state flow regime is much slower in the 3D situation than in the 2D systems examined here. The critical state regime is thus reached much later and at considerably higher dilation level in 3D. Possible reasons for this qualitative difference are discussed but more studies are needed to identify them properly.