A state variable approach is developed to simulate the isothermal quasi-static mechanical behavior of elastic- viscoplastic materials subject to small deformations. Modeling of monotonic/cyclic loading, strain-rate effect, work hardening, creep, and stress relaxation are investigated. Development of the constitutive equations is based upon Hooke\u27s law, the separation of the total strain into elastic and plastic quantities, and the separation of work hardening into isotropic and kinematic quantities. The formulation consists of three coupled differential equations; a power law measuring viscoplastic strain-rate and two first order equations for isotropic and kinematic hardening. Derivation of, behavior of, and use of the model are discussed. Actual material data from uniaxial monotonic and cyclic tests is simulated numerically. The formulation, excluding kinematic hardening, is also expanded into multiple dimensions and the compression of a cylinder with constrained ends is solved using the finite element method
