The mechanics of a circular membrane delaminating from a rigid punch is derived based on linear elasticity and an energy balance approach. Both the tensile prestress and the resulting concomitant stress upon external loading are considered. A "pull-off" phenomenon is predicted when the contact circle shrinks to a critical value between 0.1945 and 0.3679 of the film diameter, depending on the critical strain energy release rate and the prestress. These asymptotic limits match exactly with the prestress dominant model by Shanahan and prestress free model by Wan. Thin film delamination from a rectangular punch is also investigated. Unlike the circular punch, the rectangular contact is expected to reduce to a line contact with zero contact area at "pinch-off." The graphs and trends shown are useful in assessing thin film delamination assisted by a prestress.