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The de-adhesion of a thin film from a rigid substrate is studied. It is assumed, that a periodic array of micro-cracks exists along the film/substrate interface. During formation, the film expands, while being constrained by the substrate. This phenomenon leads to development of compressive stresses. Then buckling may occur and cause crack growth either along the interface or in the film towards the free surface. A finite element model has been developed, which simulates film buckling and subsequent interfacial crack growth, based on film/substrate adhesive constitutive relations. These relations have been motivated by atomistic calculations on bimaterial failure. The model does not require any facture criterion. Interfacial work of separation has a significant effect on damage growth ahead of the crack tip, along the interface. Also, a critical remote compressive stress exists, at which damage progresses without further loading of the film. The relation between the critical compressive stress for extensive damage and the interfacial work of separation can be used in combination with experiments for the quantitative characterization of the film/substrate interface.