We consider the problem of a thin smectic film placed on a periodically striped solid surface, with stripe width lambda, and with the upper surface free. The striped surface-smectic fluid interfacial energy induces the lamellae to align perpendicularly to the surface. We show that in many cases both the bulk liquid and the free upper surface will undulate to relieve the frustration caused by the stripes. In marked contrast to the traditional Helfrich-Hurault instability we show that this new instability occurs under both extension and compression. As a concrete example we consider a symmetric diblock copolymer thin film melt, with bulk equilibrium AB-BA bilayer spacing L-2. When L-2 <2 lambda these undulations will be enhanced while for L-2>2 lambda they will be diminished.