The aim of this research is to investigate numerical modeling of coupling between creep and crack growth in concrete. The paper underlines the different approaches that can be envisioned in order to incorporate damage into the time dependent creep functions: In the Maxwell model, the effective stress approach was used. In the Kelvin model, material damage acts on the time independent part of the creep functional. The numerical models are calibrated so that they fit the experimental data. Some computer simulations have been carried out. Results of various loading histories with different controlling parameters confirm the influence of the damage behaviour on creep or relaxation of concrete. Actually, the kinetics of creep in bending beams is strongly correlated with the internal length when damage occurs.