In this paper, a new constitutive model for quasi-brittle materials subjected to cyclic loadings is presented. The main features are the asymmetry between tension and compression, permanent strains and unilateral effect, ensuring not only the relevancy but also the reliability of numerical predictions. The hysteretic effects are also included in the model since their importance for seismic applications has been emphasized in the literature. The numerical implementation of the model is presented, and local tests are shown for validation. Reinforced concrete structures subjected to cyclic loading are considered to highlight the efficiency of the model.