The objective of this work is to study indentation-induced delamination of a strong film from a ductile substrate. To this end, spherical indentation of an elastic-perfectly plastic substrate coated by an elastic thin film is simulated, with the interface being modeled by means of a cohesive surface. The constitutive law of the cohesive surface includes a coupled description of normal and tangential failure. Cracking of the coating itself is not included and residual stresses are ignored. Delamination initiation and growth are analyzed for several interfacial strengths and properties of the substrate. It is found that delamination occurs in a tangential mode rather than a normal one and is initiated at two to three times the contact radius. It is also demonstrated that the higher the interfacial strength, the higher the initial speed of propagation of the delamination and the lower the steady state speed. Indentation load vs. depth curves are obtained where, for relatively strong interfaces, the delamination initiation is imprinted on this curve as a kink.