Compressively-stressed elastic films on finite-thickness viscous substrates can undergo a buckling instability that relieves stresses but destroys the planarity of the film. A linear-stability analysis is performed to determine the onset and maximally unstable mode of this buckling instability as a function of misfit strain, viscous layer thickness, and viscosity. We find that the onset of the buckling instability of the film on a glass layer is the same as that for a compressively stressed free-standing film. However, the maximally unstable wavelength increases as the glass layer thickness increases. Comparisons with experimental data are provided.

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