External bonding of fiber reinforced polymer (FRP) composites has become a popular technique for strengthening metal structures. A new concept of edge-elastic region was proposed to deal with the bonded reinforcement at present work. The expressions for interfacial shear stress distribution and failure load are derived under different load stages, accounting for inelastic behavior (plastic and softening) of the adhesive. The closed-form solution which can be regarded as an extension of trapezoidal cohesive zone model (CZM) is capable of satisfying the free shear boundary condition. Validation of the present method was performed by comparison of the interfacial elastic and plastic stress with the results of FEM and the failure load with experimental testing data. Good correlation shows that the present method can provide improved accuracy of the stress analysis, especially the peak shear stress and its location, which will further facilitate the design and optimization of the bonded reinforcement.