A critical analysis of approaches to find constitutive relations from the tests on uniaxial and two axial loading is presented. Then we report on the methodology of fitting parameters of constitutive relations for superplastic forming based on the results of cone cup and elongated wedge cup tests. Optimal cone and wedge angles are estimated analytically and also from the results of finite element simulations. Our methodology is based on comparison of the experimental results and the results of numerical simulations of the corresponding tests in frame of the commercial software such as ANSYS10.0 (ED). We carry out numerical simulations of the cone cup and the wedge cup tests for different sets of parameters of the chosen constitutive relation and different values of friction coefficient in order to reproduce the experimental results. The parameters corresponding to the best fit of the experimental data are then recommended for the use in computer simulations of the superplastic forming of commercial products.