The rehabilitation, reinforcement and repair of weak and damaged structures has become widespread in the recent years. A method for rehabilitation, reinforcement and repair of reinforced concrete structures utilizes FRP reinforcing plates. The external reinforcement with FRP plates has the problem of premature and abrupt debonding of plate from the beam surface. Several researches about debonding have been carried out at Isfahan University of Technology in the recent years. A new grooving method (EBROG) for strengthening reinforced concrete beams in flexure and shear with FRP materials has been introduced. The results indicate that the grooving method delays debonding of plate and sometimes the failure mode becomes the rupture of plate. A method for increasing the contact area between reinforcing plate and concrete beam was also introduced. In this method, FRP plates are glued directly to the surface of grooves in the tension side of the beam. With this method, the shear force is transferred to stronger parts of the concrete. This method is a combination of EBR, NSM and EBROG methods, and is called EBRIG method. EBRIG method shows favorable results. The construction of samples with real-world scale and carrying out experiments on them is a time consuming and economically expensive process. We need a method to predict ultimate load and displacement in EBRIG method with sufficient accuracy, with the possibility of predicting the occurrence of debonding. The behavior of samples reinforced with EBRIG method was investigated with a non-linear finite element model for the first time. Also, a previously developed model for EBROG method was validated for small specimens. 60 reinforced beams were numerically modeled with EBRIG method. The results show that when the thickness of reinforcing plate is high and the number of grooving rows is high, the least possible distance between groove rows gives the best results. Key Words: FRP, debonding, Externally Bonded Reinforcement On Grooves (EBROG), Externally Bonded Reinforcement In Grooves (EBRIG),Finite element model .