The fracture mechanics of adhesion tests based on the contact of a flat punch or a spherical indenter with a thin elastic layer are studied. For a flat punch, existing literature data are used to derive semi-empirical analytic expressions for the compliance of the thin film. For spherical indenters, the load-displacement relationship, in addition to values for the compliance, are obtained from finite element analysis. Preliminary experimental results on the adhesion of a spherical indenter to commercially available pressure sensitive adhesives are also described, and the fracture mechanics analysis is placed in the context of these results.