A 1-dimensional rectangular freestanding membrane clamped at opposite ends adheres to the planar surface of a rectangular punch. A tensile load applied to the punch causes the membrane to deform and gradually delaminate from the substrate. At equilibrium, the applied load is balanced by the disjoining pressure at the membrane-punch interface with range, y, and magnitude, p. Applying the Dugdale-Barenblatt-Maugis cohesive zone approximation, the disjoining pressure is taken to be uniform and confined to a finite cohesive length at the contact edge. For a fixed adhesion energy, c p y, we investigate the following: (i) the Derjaguin-Muller-Toporov (DMT) limit where y > infinity and p > 0,(ii) the Johnson-Kendall-Roberts (JKR) limit where y -> 0 and p -> infinity, and (iii) the general case for intermediate but finite y and p. Delamination continues until the contact area shrinks to a line prior to "pinch-off''. The results are compared with the 2-dimensional axisymmetric membrane counterpart.