Elastic-viscoplastic constitutive equations based on two internal state variables are utilized to determine material response for uniaxial cyclic loading conditions. These equations are capable of representing the principal features of cyclic loading behavior including softening upon stress reversal, cyclic hardening or softening, tendency toward a stable limit cycle, cyclic relaxation, and cyclic creep. Calculations were performed for various stress and strain controlled conditions using material constants intended to represent commercially pure titanium and aluminum and OFHC copper. Capabilities and limitations of the analytical formulations are discussed in relation to computed results and corresponding test data.