The available models for estimating the creep strains of concrete generally assume that concrete is a homogeneous material. Since concrete is a composite, such models are incapable of taking into account incompatible strains between the cement paste and aggregates during creep loading. The main objective of this paper is to demonstrate that microcracks could increase the creep strain level and justify the use of a coupling between creep and damage at the macroscopic scale. To achieve this objective, a viscoelastic model has been adopted to compute the creep strains of a mesostructure composed of aggregates and cement paste under varying load levels, in both tension and compression. Creep tests drawn from the literature are used to show that the microcracks generated by incompatible strains significantly increase the creep strains under high stress/strength ratios. It is then proven that the mesoscopic approach is capable of predicting concrete failure during a ring test involving basic creep. Residual Concrete behavior is also predicted and modifications observed especially following creep in compression which is not consistent with the few experimental data available meaning that apparent non-linearity cannot be completely attributed to strains incompatibilities at the mesoscale.