The paper presents a linear stability analysis to demonstrate that the nominally flat surface of an elastically stressed body is unstable to the growth of perturbations with wavelengths greater than a critical wavelength. For a solid constrained in one dimension and subjected to uniform dilatation, this critical wavelength scales as \(\lambda_c = \gamma E / \sigma^2\), where \(\gamma\) is the surface energy, \(E\) is Young's modulus, and \(\sigma\) is the nominal stress associated with the constrained dilatation. The most unstable mode depends on the manner of matter transport, specifically surface diffusion and evaporation/condensation. The predicted wavelength of instability is consistent with observations of thin InGaAs films grown on GaAs. The analysis shows that the formation of a "rough" surface profile lowers the system's energy if the wavelength exceeds \(\lambda_c\). The paper also discusses the elastic analysis and surface kinetics, including the effect of surface diffusion and evaporation-condensation on the surface evolution. The results are applied to the problem of a thin film misfitting with respect to its substrate, and the theory is compared with experimental observations of InGaAs films grown on GaAs. The predicted wavelength of instability is within a factor of two of the simplistic energy analysis, and the theory is also discussed for macroscopic solids, though such instabilities have not been observed due to the small amplitude of steady-state roughness.The paper presents a linear stability analysis to demonstrate that the nominally flat surface of an elastically stressed body is unstable to the growth of perturbations with wavelengths greater than a critical wavelength. For a solid constrained in one dimension and subjected to uniform dilatation, this critical wavelength scales as \(\lambda_c = \gamma E / \sigma^2\), where \(\gamma\) is the surface energy, \(E\) is Young's modulus, and \(\sigma\) is the nominal stress associated with the constrained dilatation. The most unstable mode depends on the manner of matter transport, specifically surface diffusion and evaporation/condensation. The predicted wavelength of instability is consistent with observations of thin InGaAs films grown on GaAs. The analysis shows that the formation of a "rough" surface profile lowers the system's energy if the wavelength exceeds \(\lambda_c\). The paper also discusses the elastic analysis and surface kinetics, including the effect of surface diffusion and evaporation-condensation on the surface evolution. The results are applied to the problem of a thin film misfitting with respect to its substrate, and the theory is compared with experimental observations of InGaAs films grown on GaAs. The predicted wavelength of instability is within a factor of two of the simplistic energy analysis, and the theory is also discussed for macroscopic solids, though such instabilities have not been observed due to the small amplitude of steady-state roughness.