We report the critical effects the deformational stress from the elastic nature of a confined polymer layer has during the relaxation process on the buckling of thin metal-polymer bilayer systems (less than 100 nm) even above the temperature at which the polymer is in the liquid flow region. In contrast with what is generally believed, the dispersion force does not play a significant role in the buckling. We also find that the final wrinkled waves take on the shape of wormlike islands. The coarsening leading to the island structure is driven by the growth in amplitude of the dominant wave at the expense of less dominant ones.