The purpose of this study is to develop an effective and robust computational scheme for the subloading-overstress elasto-viscoplastic constitutive model proposed by Anjiki and Hashiguchi [1]. The conventional overstress elasto-viscoplastic model has several shortcomings, especially in the reproducibility of the rate-dependent mechanical responses of materials. In particular, it is unable to reproduce (1) the evolution of inelastic deformation under high-speed strains, such as impact loading, and (2) the accumulation of inelastic deformation under cyclic loading with a small stress amplitude below the yield stress. Combining the concept of subloading surface with the conventional model provides a remarkable improvement in model performance, resolving the aforementioned issues and thereby making the model applicable to cyclic loading with a wider range of strain rates from quasi-static loading to impact loading. This study deals with a numerical implementation using the implicit algorithm for the subloading-overstress model, in witch we introduce improved algorithms for loading/unloading judgment and accurate updating of internal variables. For validation, the numerical code developed in this study is applied to simulate several existing experimental data of rate-dependent inelastic response of metallic materials. In addition, we present a comparative study of two classes of existing viscoplastic flow rules, where a remarkable difference in the model behavior is observed even for the same material constants.