Carbon fibre-reinforced polymers (CFRP) have been used widely as reinforcement material for degraded structures in the past decades. However, the CFRP composite is prone to debond from the substrate prematurely. An additional anchorage is usually added at the end of the CFRP-to-substrate joint to delay or even prevent its premature debonding from flexurally-strengthened beams. Therefore, the loads transmitted to the CFRP composite increase and the debonding process has some important changes compared to the case where no additional anchorages are used. Based on the singe-lap shear test, a new analytical approach is developed to facilitate the understanding of the debonding process of mechanically anchored CFRP-to-substrate joints with (or without) an end anchorage with a linear or nonlinear behaviour, which shows its wide-ranging application. Since it is simple to integrate or derivate, a well-known exponential bond-slip relationship is used in the proposed analytical approach. To validate it, some experimental tests found in the literature are used. Since it only deals with the pure mode II debonding process, the nonlinear bond behaviour of the end anchorages such as a steel plate subjected to a compression load, is modelled by the Finite Difference Method (FDM). In this latter case, another bond-slip relationship is used, which considers the influence of mode I (due to external compression) into mode II through the Mohr-Coulomb failure criterion. Despite other results and discussions that could be made, the load-slip curves obtained from each case are mainly reported and discussed here.