In this work, a finite element method was performed to simulate the spherical indentation of a ductile substrate coated by a strong thin film. Our objective was to study indentation-induced delamination of the film from the substrate. The film was assumed to be linear elastic, the substrate was elastic–perfectly plastic, and the indenter was rigid. The interface was modeled by means of a cohesive surface. The constitutive law of the cohesive surface included a coupled description of normal and tagential failure. Cracking of the coating itself was not included. During loading, it was found that delamination occurs in a tangential mode rather than a normal one and was initiated at two to three times the contact radius. Normal delamination occurred during the unloading stage, where a circular part of the coating, directly under the contact area was lifted off from the substrate. Normal delamination was imprinted on the load versus displacement curve as a hump. There was critical value of the interfacial strength above which delamination was prevented for a given material system and a given indentation depth. The energy consumption by the delamination process was calculated and separated from the part dissipated by the substrate. The effect of residual stress in the film and waviness of the interface on delamination was discussed.