In this paper, a numerical simulation is presented on the behavior of concrete beams, reinforced with pre-stressed CFRP. The numerical results are compared to experimental results. Non-linear material behaviour is considered, namely: the inelastic compressive concrete behaviour, the elasto-plastic behaviour of steel reinforced bars, the bond-slip relationship between the concrete and the internal steel reinforced bars, the mode-II fracture interface between the concrete and the pre-stressed CFRP and concrete cracking. Cracking in concrete is modelled according to a discrete strong discontinuity approach, in which the discontinuities are embedded within the finite elements. A sequentially-linear approach is adopted in order to avoid non-convergence problems. The present analysis aims at trying to better understand the failure mechanisms found in the experimental tests; these mechanisms will be discussed in a final section of the paper.