Abstract:bstract: The description of constitutive relationship of materials up to failure plays important role in the large deformation analysis and fracture mechanism study. The true stress and strain curves obtained by traditional tensile test become immeasurable after necking. This paper presents a new method to determine full-range uniaxial constitutive relationship of ductile material by tensile testing on a funnel-shape specimen, and using DIC(Digital image correlate)technology which could accurately measure mechanical 3D displacement and strain and finite element analysis(FEA). This method is abbreviated TF(Test and FEA)method in this study. Taking full-range constitutive relationships as constitutive relationships in finite element software material storage. The FEA results for the funnel specimens show that, the simulated load versus displacement curve, diameter at the funnel root versus displacement curve and funnel deformation contours and simulated surface strain distribution nephogram are closed to test results. The full-range true stress and strain curves obtained by funnel specimens with different radius are good coincident with each other. In addition, the mechanical behaviors on the cross section of the funnel specimens are discussed. The parameters of constitutive relationships and breaking stress and strain for 304 stainless steel are given.