A circular membrane clamped at the periphery is allowed to adhere to or to delaminate from a planar surface of a cylindrical punch in the presence of intersurface forces with finite range and magnitude. Assuming a uniform disjoining pressure within the cohesive zone at the delamination front, the adhesion-delamination mechanics is obtained by a thermodynamic energy balance. Interrelations between the instantaneous applied load, punch displacement, and contact circle, and the resulting critical thresholds of “pinch-off,” “pull-off,” and “pull-in” are derived from the first principles. Two limiting cases are obtained: (i) intersurface force with long range and small magnitude in reminiscence of the classical Derjaguin–Muller–Toporov (DMT) model and (ii) short range and large magnitude alluding to the Johnson–Kendall–Roberts (JKR) model. The DMT-JKR transitional behavior has significant impacts on adhesion measurements, micro-electromechanical systems, and life-sciences.