Abstract: By Complex Mapping theory, doing mutual numerical calculation to finite odd and even interpolation points on the non-circle cross-section profile of special-shaped products, the conformal mapping function which can mutually transform cross-section region into unit dish region is set up. Translating the extrusion forming of special-shaped products into two-dimension problem, plastic stream function is determined, and the mathematical models of die cavity surface with various vertical curves are built up. Using the upper bound method, three types of vertical curves and their optimized parameters of die cavity are compared. Taking ellipse-shaped products as examples, their analysis and optimization are carried out.