On the basis of Conformal Mapping theory, using approaches of numerical trigonometric interpolation and vector normal convergence, region function of three-dimension deforming, surface function of die cavity, and mapping function between the plastic flow model and the axis-symmetry model were set up respectively for fine extruding special-shaped products with different arc radius ri. Then the stream function and both fields of velocity and strain ratio are inferred for special-shaped plastic deformation; meanwhile, with the help of Upper-Bound principle, the parameter of die cavity gets optimized. Taking square-shaped and hexagon-shaped products with different arc radius ri as examples,the velocity field gets analyzed, the parameter of die cavity is optimized and the die cavity gets depicted as well. Consequently, above study provides theoretical support for achieving the technical goal of CAD/CAM integration in die cavity of fine extrusion.