A linear elastic fracture mechanics (LEFM) approach to the debonding analysis of concrete beams strengthened with externally bonded fiber-reinforced-polymer (FRP) strips are studied. The analytical models based on the LEFM approach are presented and discussed. The fracture analysis has adopted the energy-release-rate approach and the J-integral formulation. In addition, an algorithm for the construction of the equilibrium path that describes the debonding process in the FRP strengthened beam has been developed. The approach and its applicability to the debonding analysis of the FRP strengthened beam has been examined through three cases that include a single shear test, an edge peeling test, and a beam specimen strengthened with FRP. In cases where qualitative information regarding the initiation and progress of the debonding process is available, the LEFM model can be used for a reasonable quantitative appraisal of the debonding mechanism.