The effects of externally bonded composite plates on the mechanical behaviour of a cracked RC beam loaded in flexure are modelled by a multi-scale approach. The problem of crack width prediction is addressed. Firstly, the state-of-the-art methods for crack width prediction in concrete beams are recalled. Then, they are confronted to experimental data obtained with a full-field optical method. It is shown that classical models are not suited for the prediction of crack widths in repaired beams. In order to improve the modelling, a new approach is considered: the structural behaviour of the beam is assessed from numerical computations conducted over a relevant representative volume element. The contribution of this multi-scale approach is that input parameters have a physical meaning and that the results are consistent with full-field measurements conducted on repaired beams. Finally, the paper focuses mainly on the validation of the model for computing displacement fields, crack widths and curvatures in repaired beams. The benefit for the identification of bonding properties between the composite sheet and concrete is also pointed out.