In　this　paper,　by　a　semi-analytical　method,　the　propagation　characteristics　of　shear　horizontal　surface　acoustic　waves　in　semi-infinite　superlattices　containing　viscous　materials　are　investigated.　The　factors　that　influence　the　attenuation　and　phase　velocity　of　the　surface　waves　are　analyzed　in　detail.　The　results　may　be　useful　for　the　design　of　acoustic　wave　devices.　(C)　2010　Elsevier　B.V.　All　rights　reserved.