Summary: In this paper a method is developed in order to find tensorial constitutive equations based upon empirical uni-axial constitutive relations found in experimental investigations. For engineering applications it is very important to generalize uni-axial relations to multi-axial states of stress. This can be achieved by using interpolation methods for tensor functions, as pointed out in detail in the paper. It can be shown, that the scalar coefficients in tensorial constitutive equations are functions of invariants and experimental data. Some examples are discussed. For instance, the Norton-Bailey creep law, a uni- aixal damage relation, and the Ramberg-Osgood stress-strain relation are generalized to tensorial constitutive equations. Other nonlinear empirical relations can be generalized in the same manner. Furthermore, the elastic-plastic transition is discussed.