An　input　method　of　obliquely　incident　earthquake　for　a　layered　site　with　step-shaped　topography　is　developed　based　on　the　viscous　boundary　and　the　horizontal　layered　site　response　analysis　method　under　obliquely　incident　earthquake.　The　input　wave　fields　at　lateral　boundaries　are　the　free　field　responses　of　a　horizontal　layered　site.　Each　lateral　boundary　uses　the　site　with　identical　parameters　as　a　lateral　boundary,　and　therefore　two　lateral　boundaries　use　the　different　site　models.　The　input　wave　field　at　the　bottom　boundary　is　an　incident　wave　field.　Because　above　treatments,　the　input　method　is　approximate.　The　factors　affecting　the　accuracy　of　the　method　have　been　discussed,　such　as　boundary　location,　inputted　earthquake,　the　angle　of　incidence,　slope　inclination,　and　layered　media.　The　results　indicate　that　the　peak　error　of　displacement　is　less　than　5%　for　all　kinds　of　cases　studied　in　this　paper　under　the　SV　wave.　The　accuracy　of　the　proposed　input　method　of　obliquely　incidence　earthquake　satisfies　the　engineering　requirements,　and　the　method　can　be　used　for　seismic　response　analysis　of　a　step-shaped　topography　site.　©　2019,　Engineering　Mechanics　Press.　All　right　reserved.