Deformation of rubber and poly(ethylene terephthalate) coated with a platinum or a gold film was studied. The thickness of the coating film was approximately ten nanometers. The polymer substrates were 10(4) to 10(5)-fold softer than the coating. Folding of the coating leading to the appearance of a wave-like pattern on an originally smooth surface was observed both in tension and after shrinkage. In tension the wave crests are oriented along the elongation direction. After shrinkage the wave crests are perpendicular to the shrinkage direction. For rubber substrates, the appearance of the wave is explained by a mechanical buckling instability of the coating under compressive force. The length of the surface wave depends on the thickness of the coating layer and the rigidity of the polymer substrate. In addition to folding, regular fragmentation of the coating film on long and comparatively narrow bands is observed. The cracks are perpendicular to the wave crests both in tension and after shrinkage.