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In the mechanics of porous and powder materials the system of equations comprising the pyramid yield criterion together with the stress equilibrium equations under conditions of axial symmetry forms a statically determinate system at edge regimes. The results presented here for this system are consequently independent of any flow rule that may be chosen to calculate the deformation and also independent of whether elastic strains are included. The stress equilibrium equations are written relative to a coordinate system in which the coordinate curves coincide with the trajectories of the principal stress directions. Then, a method of finding the trajectories of the principal stresses is developed.