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A plate with a crack, repaired by an adhesively bonded overlay of a finite strip, is investigated. In the analysis model it is assumed that due to high stress concentration an internal debonding between the strip and the plate may generate from the crack surfaces or, in other words, it is assumed that the strip may be originally designed to be adhesively bonded partially instead of fully, to the cracked plate. With the aid of the Green functions for a pair of edge dislocations and for a concentrated body force, a singular integral equation method is presented, by which the stress singularities not only at the crack tips but also at the strip ends, and at the internal debonding fronts or the internal edges of the partly bonding areas, can be examined. The numerical results given show the effects of various geometric and material parameters, defining, respectively, the relative size and position of the strip to the crack, the distances of the internal debonding fronts or the internal bonding edges away from the crack surfaces, and the relative stiffness of the strip to the plate, on the stress intensity factors at all the three types of singular points.