A combined experimental/finite element effort is carried out to elucidate the post buckling response of unilaterally constrained plates under monotonically increasing edge thrust. Real time observations, together with a wide range of plate aspect ratio and a large load level facilitate deep physical insight into the general behavior of this class of problems. The interaction of the plate with the rigid restraining plane following buckling leads to interesting deformation sequences, characterized by the development of asymmetric bulges and contact zones following by a possible plate snapping. The latter is motivated by a secondary buckling evolving gradually from a contact zone(s) or a bulge(s). These two instability mechanisms are competitive, being dictated by the plate aspect ratio and other system parameters. The critical load for plate snapping agrees well with a finite element prediction based on an asymmetric deformation choice that minimizes the strain energy in the plate. A semi analytic relation for predicting the onset of secondary instability in the contact area and subsequent plate snapping is developed based on the numerical results. Finally, the present work seems to add a new dimension into the fracture of coatings and laminated composites containing near-surface defects.