External bonding of fiber reinforced polymer (FRP) composites has become a popular technique for strengthening concrete structures all over the world. The performance of the interface between FRP and concrete is one of the key factors affecting the behavior of the strengthened structure, and has been widely studied using simple shear tests on FRP plate/sheet-to-concrete bonded joints. While a great deal of research is now available on the behavior of these bonded joints, no closed-form analytical solution has been presented which is capable of predicting the entire debonding propagation process. This paper presents such an analytical solution, in which the realistic bi-linear local bond-slip law is employed. Expressions for the interfacial shear stress distribution and load-displacement response are derived for different loading stages. It is also shown how experimental loaddisplacement responses of these joints can be used to quantify interfacial properties, including the interfacial fracture energy and parameters of the local bond-slip relationship. The debonding process is discussed in detail and the analytical results are compared with experimental data. Finally, results from the analytical solution are presented to illustrate how the bond length and the plate stiffness affect the behavior of such bonded joints. While the emphasis of the paper is on FRP-to-concrete joints, the analytical solution is equally applicable to similar joints between thin plates of other materials (e.g. steel and aluminum) and concrete.