Abstract: This paper combines the internal variable theory and thetensor function representation theory to establish the constitutiveequations of the deformation theory and the increment theory for theisotropic and rate independent materials. In the equations, there are threecomplete and irreducible base tensors, that is, the stress tensor of thezero order, the first order and the second order power, to show that theprincipal axes of plastic strain and its increment are coincident with thoseof the stresses. With the orthogonalization of the base tensors, thegeometrical explanation of the constitutive equations is obtained in theprincipal stress space. Furthermore, the coefficients in the constitutiveequations of deformation theory (or increment theory) can be derived withthree invariants of stresses and plastic strain ( or plastic strainincrements). Meanwhile, the present constitutive equations may reduce toclassical deformation theory (or plastic potential theory), and beconsistent to the singular yield surface theory.