SummaryIntegration of stress‐strain‐time relationship is a key issue for the application of elasto‐viscoplastic models to engineering practice. This article presents a novel adaptive substepping cutting‐plane time integration scheme for elasto‐viscoplastic models keeping the advantage of original cutting‐plane (OCP) with only the first derivatives of loading surface required. The deficiency of OCP time integration algorithm is first discussed taking a simple overstress theory based elasto‐viscoplastic modified Cam‐Clay model (EVP‐MCC) as example. To overcome this, a new algorithm is developed with three features: (1) an evolution function for the hardening variable of dynamic loading surface is innovatively deduced for the Taylor series approximation, (2) the elastic predictor is modified to account for the initial viscoplastic strain rate with more accuracy, and (3) a new adaptive substepping technique for restricting simultaneously both strain and time incremental sizes based on the overstress distance is proposed. For easy understanding, the proposed algorithm is first presented for one‐dimensional condition, and then extended to three‐dimensional condition. The new integrated EVP‐MCC model using the proposed algorithm is examined by simulating laboratory tests at both levels of integration point and finite element with a good performance in terms of accuracy and convergence.