Abstract In the past decade or so, a substantial body of work on state variable constitutive equations for elasto-viscoplasticity has appeared in the literature. Such constitutive equations are known to be numerically very stiff. In this paper we formulate a fully implicit, Euler backward time-integration procedure for a set of internal variable constitutive equations for isothermal, isotropic elasto-viscoplasticity with isotropic hardening. The time-integration procedure is a generalization of the well-known “radial-return” algorithm of classical rate-independent plasticity, and it should therefore be well suited for implementation in large-scale finite element codes. As an example, we have implemented the procedure in the finite element code ABAQUS, and using a set of specific constitutive equations, we show the results of two sample problems.