A cohesive zone modeling (CZM) approach with a bilinear traction-separation relation is used to study the peeling of a thin overhanging plate from the edge of an incompressible elastomeric layer bonded firmly to a stationary rigid base. The deformations are approximated as plane strain and the materials are assumed to be linearly elastic, homogeneous, and isotropic. Furthermore, governing equations for the elastomer deformations are simplified using the lubrication theory approximations, and those of the plate with the Kirchhoff–Love theory. It is found that the peeling is governed by a single nondimensional number defined in terms of the interfacial strength, the interface fracture energy, the plate bending rigidity, the elastomer shear modulus, and the elastomeric layer thickness. An increase in this nondimensional number monotonically increases the CZ size ahead of the debond tip, and the pull-off force transitions from a fracture energy to strength dominated regime. This finding is supported by the results of the boundary value problem numerically studied using the finite element method. Results reported herein could guide elastomeric adhesive design for load capacity and may help ascertain test configurations for extracting the strength and the fracture energy of an interface from test data.