A quantitative analysis based on the Luryi and Suhir model [Appl. Phys. Lett. 49, 140 (1986)] has shown that the growth of strain relaxed and low dislocation density SixGe1−x and InxGa1−xAs buffer layers on Si and GaAs substrates, respectively, is feasible despite the layer/substrate lattice mismatch. A successful growth of such layers is possible on partially masked substrates by selective lateral overgrowth method. In this case, the buffer layer/substrate misfit stress is of limited lateral extent, in accordance with Saint‐Venant’s principle, and its effective length does not exceed 15% of the seeding window width even for very thick buffer layers. High threading dislocation density in the buffer layer can be avoided by reducing the window width such that the effective stress zone length is comparable with the critical layer thickness for misfit dislocation formation. However, a thin alloy layer deposited by molecular beam epitaxy or metalorganic chemical vapor deposition on both the Si and GaAs substrates, prior to coating with SiO2 mask and patterning with oxide‐free seeding windows, is required for a quite broad range of alloy compositions © 1995 American Institute of Physics.