The adhesion of a punch to a linear elastic, confined layer is investigated. Numerical analysis is performed to determine the equivalent elastic modulus in terms of layer confinement. The size of the layer relative to the punch radius and its Poisson's ratio are found to affect the layer stiffness. The results reveal that the equivalent modulus of a highly confined layer depends on its Poisson's ratio, whereas, in contrast, an unconfined layer is only sensitive to the extent of the elastic film. The solutions of the equivalent modulus obtained from the simulations are fitted by an analytical function that, subsequently, is utilized to deduce the energy release rate for detachment of the punch via linear elastic fracture mechanics. The energy release rate strongly varies with layer confinement. Regimes for stable and unstable crack growth can be identified that, in turn, are correlated to interfacial stress distributions to distinguish between different detachment mechanisms.