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A mathematic model of unsteady aluminum extrusion process simulation using body-fitted grids based finite volume method (FVM) was studied and built in this paper. Body fitted grids were used to fit curved face boundaries, so arbitrary complex geometries can be well matched. Control equations were discretized on body fitted grids directly using Cartesian coordinates, so complicated coordinate translation can be avoided. Considering non-orthogonality of body fitted grids, deferred correction technology was adopted to filter out the pressure oscillations by generating pressure difference between adjacent nodes, as well as to eliminate the errors caused by non-orthogonality of grids, and then SIMPLE method based on body fitted grids was built based on above all. A program had been written and a typical process of aluminum extrusion was simulated, amount of physical fields such as velocities, effective stress and effective strain rate etc. were obtained, the results were compared with that simulated by finite element method, so the feasibility and exactness of the mathematic model is proved.