The grooving method in the form of “externally bonded reinforcement on groove” (EBROG) has been in recent years introduced as an alternative method of the conventional externally bonded reinforcement (EBR) for strengthening concrete structures using fiber reinforced polymer (FRP) materials. The present research is a first attempt to develop an FRP-concrete bond strength, effective bond length and bond-slip models based on nonlinear regression on experimental results. For this purpose 154 single lap-shear tests are conducted on 136 specimens made through the EBROG method and 18 specimens through the EBR method. Design of Experiments techniques in the form of response surface methodology and I-optimality criteria are used to design and optimize tests layout. The strain and stress fields on the FRP bond area are analyzed using the image processing technique of particle image velocimetry (PIV). The effects of groove dimensions, concrete compressive strength, as well as FRP sheet width and stiffness on the EBROG performance and its efficiency are investigated and compared with those on similar EBR specimens. Also 7 reinforced concrete beams with dimensions of 2600×300×200 mm were strengthened with FRP sheets and were tested. Beams were designed in a way under which the EBR and EBROG methods can be compared considering different groove dimensions and patterns. Although debonding failure is observed to occur in all the specimens, the results obtained confirm the superiority of the EBROG over the EBR specimens as evidenced by an average enhancement of 31% and 24% achieved in load bearing capacity in single lap-shear and beams tests, respectively. Finally the agreement of the proposed modelto data is verified by different statistical tools and analysis of variance. The correlation between RC beams and single lap-shear results were made. Keywords: Fiber reinforced polymer (FRP); Bond strength; Effective bond length; Bond-slip; Externally bonded reinforcement on groove (EBROG); Single lap-shear tests.