The technique of bonding fibre reinforced polymer (FRP) composites to the tension face or sides of reinforced concrete (RC) beams has become very popular for strengthening or retrofitting purposes. A distinct characteristic of such strengthened RC beams is that they very often fail due to various premature debonding failures. This paper presents a fracture mechanics based finite element analysis of debonding failures. Numerical results for an experimental beam are presented. Initial findings show that the method can successfully simulate the concrete cover separation failure mode in FRP strengthened RC beams.