The mathematic model of 3D aluminum extrusion processes using finite volume method (FVM) was established in this paper. The basic theories and rigid-plastic flow theories of this model were researched and built. Non-orthogonal structured grids were used to match complex geometric boundaries and local refinement of grids was also realized. The collocated arrangement is used to discretize the governing equations on non-orthogonal grids directly, pressure oscillations bring by this arrangement and error caused by grid’s non-orthogonality is eliminated by special treatment. A pocket die extrusion process was simulated using the program developed in this paper. The simulation results were also compared with that simulated by FEM software Deform in the same process, material and die conditions. The feasibility and efficiency of the mathematic model built in this paper was demonstrated by the simulation results and the comparison.