Optical microscopy and atomic force microscopy were used to study a mechanically induced wrinkling instability in thin film poly(caprolactone)/polystyrene and poly(ethylene oxide)/poly(methyl methacrylate) bilayers. The instability in these samples was shown to be driven by changes in the interfacial area between a semicrystalline polymer underlayer and a glassy polymer capping layer that occurred when the underlayers were melted. The wrinkling instability resulted in the formation of one-dimensional corrugations at the surface of the bilayer samples that had a well-defined wavelength on the micrometer length scale. A linear stability analysis was used to derive a simple model of the wrinkling process in these samples. This model considered the flow and deformation of material in the molten underlayer as well as the balance of stresses in the glassy polymer capping layers. Rheological data were also obtained from polymers similar to those used to form the bilayers. These data were used to show that the model is capable of quantitatively predicting the capping layer and underlayer thickness dependencies of the characteristic wrinkling wavelengths, if the mechanical properties of the two layers and the strain in the capping layers can be determined.