This paper is concerned with a special class of response functions for some of the constitutive equations in the nonlinear isothermal theory of elastic-plastic materials. Detailed attention is given to the development of special forms for the free energy and the stress response, motivated mainly by the mechanical behavior of ductile metals in the plastic range and in the presence of finite strains. After obtaining a properly invariant representation for the free energy response (and hence also for the stress) as a function of certain (easily interpretable) measures of deformation, the results are specialized to isotropic materials and are expressed in terms of the invariants of kinematic measures. Some special cases are elaborated upon and, by way of illustration, the influence of plastic deformation on the material properties of the stress response in a simple tension test is discussed.