The debonding mode of failure, which is observed in girders strengthened using externally attached fiber-reinforced polymer (FRP) sheets, is studied in this paper. A numerical analysis of the direct-shear response of FRP attached to concrete substrate is performed to study the initiation, formation, and propagation of an interfacial crack between the two adherents. The material response of the bimaterial interface, which includes postpeak softening, is incorporated into the numerical model. The load response obtained numerically is shown to be in close agreement with that determined experimentally from direct shear tests on concrete blocks strengthened with FRP sheets. An instability in the load response is predicted close to failure and the arc-length method is used to obtain the entire load response past the displacement-limit point. The instability in the load response is shown to be a result of snapback, where both the load and the displacement decrease simultaneously. The effect of the bonded length on the stress transfer between the FRP and concrete and on the ultimate failure is also analyzed. It is shown that there is a scaling in the load capacity when the bonded length does not allow for the establishment of the full stress-transfer zone associated with interface crack growth. From the results of the numerical analysis, a fundamental understanding of interfacial crack propagation and instability at failure in concrete members strengthened using externally bonded FRP is developed. Using a simple energy based formulation; it is shown that in strengthened girders, the instability at complete debonding of FRP from concrete translates into an explosive failure associated with a sudden release of energy. © 2007 ASCE.