Bonding of fiber reinforced polymers (FRP) with epoxy layer has considered as a new structural strengthening technology in response to need for repair and strengthening of reinforced concrete structures and propagated in the last decade. Although epoxy bonding of FRP has many advantages, there is a common problem; before receiving the expected flexural capacity, most of the failure modes of these beams occur in a brittle manner, without any serious indication. The most commonly reported failure modes include ripping of the concrete cover and interfacial debonding. In the most researches who have studied the behavior of retrofitted structures, the effect of the interfacial behavior has been ignored. Proper prediction of flexural capacity of FRP strengthened of concrete beams in debonding modes is led to economical benefits in projects.In this article, the results have been verified with 6 beams in laboratory that have been loaded in two symmetric points load and divided to groups A and B. The beams had the same section, length and number of CFRP layer in each group, but thickness of CFRP was different. A nonlinear modeling with Finite Element (FE) method with the help of Abaqus is done, for investigation of real behavior of CFRP strengthened concrete beams and interfacial shear stresses concentration at CFRP cut off region, with presenting the failure theory and criterion and a method for cohesive layer simulation. Moreover the FE results are verified with an accurate experimental test results. The FEM results agreed well with the experiments, when using the cohesive model regarding failure modes, load capacity, force-displacement curves results and CFRP strains.