The adhesion between a rigid flat-end cylindrical punch and an incompressible elastic film deposited on a rigid substrate is studied. The contact interfaces between the punch and the elastic film and between the elastic film and the rigid substrate are either free to slide over one another (frictionless or slip boundary condition) or locked together (perfectly bonded or stick boundary condition). The solutions for these cases are the upper and lower bounds for the real situation in which the contact interfaces are neither frictionless nor perfectly bonded. By use of a thermodynamic method with the assumption that the detachment starts at the periphery so that the contact area remains circular all the time, the pull-off force to separate the rigid cylindrical punch from the elastic layer is obtained. The results show that the pull-off force strongly depends on the contact conditions at the interfaces.