A cohesive zone model is used to study the pull-off of a rigid flat cylindrical punch of radius c from an elastic layer of thickness h. The adhesion between the punch and the elastic layer is assumed to be sufficiently weak so that pull-off occurs by the growth of a crack from the edge of contact. Our result shows that the pull-off stress, when normalized by the interfacial strength a., depends on a single dimensionless parameter chi(f) = sigma(o)(2)c(1-v(2)) g(xi)/2 pi EWad, where E and v are the Young's modulus and Poisson's ratio of the elastic layer, respectively, Wad is the work of adhesion, and g() is a known dimensionless function of xi equivalent to c/h. chi(f) can be viewed as a generalized Tabor parameter. It characterizes the transition from a "brittle" or flaw sensitive failure regime to a "ductile" or flaw insensitive regime. The result in this work is used to generalize Maugis' theory of adhesive contact to the case where the elastic substrate is of finite thickness. (c) 2005 Wiley Periodicals, Inc.