External bonding of steel or FRP plates to reinforced concrete (RC) structures has been a popular method for strengthening RC structures; however, unexpected premature failure often occurs due to debonding between the concrete and the epoxy. We proposed a Coulomb criterion with a constant failure surface as the debonding failure criterion for the concrete-epoxy interface. Diagonal shear bonding tests were conducted to determine the debonding properties that were related to the failure criterion, such as the angle of internal friction and the coefficient of cohesion. In addition, an interface element that utilized the Coulomb criterion was implemented in a nonlinear finite element analysis program to simulate debonding failure behavior. Experimental studies and numerical analysies on RC beams strengthened by an externally bonded steel or FRP plate were used to determine the range of the coefficient of cohesion. The results that were presented prove that premature failure loads of strengthened RC beams can be predicted with using the bonding properties and the finite element program with including the proposed Coulomb criterion.