Transmission rates and dispersion relations ofSHphonons in a (111) superlattice are calculated. Unlike the case of a (100) superlattice, phonon stop bands appear inside the folded Brillouin zone in general rather than at the center and edges. A superlattice structure factor is introduced appropriately for phonon reflection or Bragg conditions in the superlattice. More importantly, the transfer matrix contains information not only about the dispersion relation, but also about the condition for frequency bands or stop bands in the dispersion relation, and the extinction rule for the Bragg reflection. The locations of the stop bands inside of the folded zone are defined as a function of frequency and incidence angle of the phonons.