Selective epitaxial growth of GaAs on a Si substrate with (GaAs)m(GaP)n strained short-period superlattices (SSPSs) and GaP buffer layer was achieved by molecular beam epitaxy under atomic hydrogen irradiation. The selective epitaxial layers were grown two dimensionally so that reflection high-energy electron diffraction patterns maintained streaky patterns with no apparent transition to three-dimensional spot patterns during the selective epitaxial growth of the GaAs/SSPSs/GaP/Si structure. Therefore, generation of threading dislocations due to the three-dimensional island growth was suppressed, in spite of a large lattice mismatch. It was also confirmed that the thickness of each buffer layer was slightly increased near the edge of the masked region. Finally, the epitaxial patterns of GaAs clearly exhibit crystal facets. © 2004 American Vacuum Society.