A linear stability analysis is presented to show that the flat surface of an elastically stressed solid is unstable to perturbations with wavelengths greater than a critical value. For a solid constrained in one dimension and subjected to uniform dilatation, the critical wavelength scales as γE/σ², where γ is surface energy, E is Young's modulus, and σ is the nominal stress. The most unstable mode depends on the transport mechanism (surface diffusion or evaporation/condensation). The predicted critical wavelength matches observations of thin InGaAs films on GaAs. The analysis considers the energy change when transitioning from a flat surface to a rough surface profile. The energy change is given by ΔF = -σ²/2E * cλ/2 + 2γc, showing that a rough surface lowers the energy if the wavelength λ > 8γE/σ². This indicates that the surface may be unstable. A more rigorous kinetic stability analysis shows that flat surfaces of elastically stressed solids are unstable to surface undulations with wavelengths greater than a critical wavelength λc. The critical and most unstable wavelengths depend on the transport mechanism. For surface diffusion, the most unstable wavelength is (4/3)λ0, while for evaporation/condensation, it is 2λ0, where λ0 = πMγ/σ². These results are consistent with observations of thin semiconductor films. The results are applied to the growth of InGaAs films on GaAs, where the predicted most unstable wavelength of 9 nm is within 50% of the observed value. The theory also predicts a maximum unstable wavelength of about 5 mm for macroscopic solids like Ni, suggesting such instabilities should be observable. However, such observations have not been made, possibly due to the small amplitude of the roughness. The analysis provides insights into the stability of stressed solid surfaces but does not determine the exact morphology of the surface.A linear stability analysis is presented to show that the flat surface of an elastically stressed solid is unstable to perturbations with wavelengths greater than a critical value. For a solid constrained in one dimension and subjected to uniform dilatation, the critical wavelength scales as γE/σ², where γ is surface energy, E is Young's modulus, and σ is the nominal stress. The most unstable mode depends on the transport mechanism (surface diffusion or evaporation/condensation). The predicted critical wavelength matches observations of thin InGaAs films on GaAs. The analysis considers the energy change when transitioning from a flat surface to a rough surface profile. The energy change is given by ΔF = -σ²/2E * cλ/2 + 2γc, showing that a rough surface lowers the energy if the wavelength λ > 8γE/σ². This indicates that the surface may be unstable. A more rigorous kinetic stability analysis shows that flat surfaces of elastically stressed solids are unstable to surface undulations with wavelengths greater than a critical wavelength λc. The critical and most unstable wavelengths depend on the transport mechanism. For surface diffusion, the most unstable wavelength is (4/3)λ0, while for evaporation/condensation, it is 2λ0, where λ0 = πMγ/σ². These results are consistent with observations of thin semiconductor films. The results are applied to the growth of InGaAs films on GaAs, where the predicted most unstable wavelength of 9 nm is within 50% of the observed value. The theory also predicts a maximum unstable wavelength of about 5 mm for macroscopic solids like Ni, suggesting such instabilities should be observable. However, such observations have not been made, possibly due to the small amplitude of the roughness. The analysis provides insights into the stability of stressed solid surfaces but does not determine the exact morphology of the surface.