Closed annular adhesive interfaces are commonly found in nature as well as in many existing and developing technologies. Such contacts provide enhanced control of interfacial history by prescribing whether interfacial separation occurs at the outer or inner edge, and whether internal pressure affects the required force for separation. To facilitate the development of technologies involving annular contacts, we have experimentally measured the relationship between applied displacement, resulting force and internal pressure, and annular interface dimensions for the contact between a rigid annular probe and an adhesive layer with finite thickness. Experiments were validated by finite element analysis models, which were used to develop semi-empirical analytical relationships for the changes in contact compliance as a function of material properties and geometric constraints. Additionally, the change in internal pressure was modeled as a function of annular contact dimensions and adhesive layer material properties. This model predicts the critical volume where internal pressure changes alters critical force for separating an annular contact interface. The results discussed here provide a foundation for new experimental protocols for characterizing soft materials, including pressure-sensitive adhesives, as well as guidelines for designing annular interfacial materials with controlled separation histories.