The strengthening of concrete structures by means of externally-bonded fibre reinforced polymers (FRPs) is now routinely considered as a viable alternative to the rather costly replacement of these structures. Previous laboratory investigations of this strengthening technique for concrete beams in flexure and shear have shown that, despite its capability of considerably enhancing the strength capacities of the beams, premature failures by debonding can often limit the effectiveness of this method. In order to prevent this type of premature failure, several anchorage schemes have been suggested. However, at present, our basic understanding of the interfacial mechanics between the concrete and the bonded FRP for such reinforcements is rather limited. In this paper, a finite element model is developed to address the interfacial behaviour of FRP-concrete joints. We present results from a finite element analysis on carbon FRP (CFRP) and glass FRP (GFRP)-concrete joints subjected to direct shear. The element sizes of the FRP, adhesive and concrete at the interface were chosen very small (0.5mm) so that the debonding behaviour can be properly investigated. A nonlinear constitutive model is utilized for plain concrete in compression. In addition, a bilinear ascending-descending constitutive relation (tension stiffening model) is used to model the material behaviour of concrete in tension. The interfacial behaviour is modelled using truss elements connecting the concrete block to the FRP sheets. The truss elements possess a nonlinear constitutive relationship between the interfacial shear stress and slip. The finite element results discussed in the paper include the ultimate capacity of the joint and the stress and strain distributions in the FRP, adhesive layer and concrete. A special emphasis is placed on the strain distribution in the FRP, the peeling-off stresses in the adhesive, and the shear stresses in the concrete layer adjacent to the interface. Comparisons between the finite element analysis and available experimental results are presented.