SummaryThe subloading surface model released from a purely elastic domain is capable of describing not only monotonic but also cyclic loading behaviors accurately. It is expected that elastoplastic deformation analyses can be performed with high accuracy and efficiency by the complete implicit stress integration algorithm with a return‐mapping projection. Various implicit stress integration algorithms for the subloading surface model have been proposed. However, they are applicable only to the monotonic loading behavior since they adopt the incorrect loading criterion presuming that the subloading surface expands in the plastic loading process. In fact, however, the plastic strain rate is induced even when the subloading surface contracts in the elastic trial step. Therefore, erroneous results in the descriptions of unloading‐reloading and cyclic loading behaviors are caused in the calculations with the existing algorithms. The complete implicit stress integration method is formulated adopting the rigorous loading criterion and implemented in Abaqus in this study. Numerical analyses for the elastoplastic deformation behaviors in the single‐element are performed by the present and the existing algorithms. In addition, the deformation analysis of the R‐notched cylinder is performed by the present algorithm. High performability of the present algorithm is confirmed by these numerical calculation results.