The goal of the present work is to identify and model the elastic–viscoplastic behavior of electrodeposited copper films under tension–compression loadings. From the experimental point of view, as proposed in the literature, a film of copper is electrodeposited on both sides of an elastic compliant substrate. The overall specimen is next subjected to tensile loading–unloadings. As the substrate remains elastic, the elastic–plastic response of copper under cyclic loading is experimentally determined. A clear kinematic hardening behavior is captured. To model the mechanical response, a new elastic–viscoplastic self-consistent scheme for polycrystalline materials is proposed. The core of the model is the tangent additive interaction law proposed in Molinari (2002). The behavior of the single grain is rate dependent where kinematic hardening is accounted for in the model at the level of the slip system. The model parameters are optimized via an evolutionary algorithm by comparing the predictions to the experimental cyclic response. As a result, the overall response is predicted. In addition, the heterogeneity in plastic strain activity is estimated by the model during cyclic loading.