This paper develops a modeling method with an incremental stress–strain–environment constitutive model to predict the change in the plastic mechanical behavior of concrete caused by environmental action. The model regards the environmental factor as a constitutive variable, similar to stress and strain. The yield condition of the model is a function of stress, the plastic internal variable, and the environmental variable. The loading–unloading criterion is established in the space constructed by the strain and the environmental variable to determine the contribution of mechanical loads and environmental factors to plastic deformation. By considering the strain rate as an environmental factor and applying the proposed method, a stress–strain–strain rate constitutive model of concrete is developed to describe the plastic flow caused by the combined action of stress and strain rate. In addition, constant- and variable-strain rate loading tests are performed to evaluate the performance of the established model. In particular, the model’s capabilities are further highlighted by comparing the simulation results of the dynamic stress–strain model and the proposed model under loading conditions with rapidly decreasing strain rates.