The　influence　of　obliquely　incident　seismic　wave　on　the　seismic　responses　of　large　and　long-span　structures　need　to　be　considered　in　seismic　design.　Based　on　a　1D　time-domain　method　for　the　out-of-plane　wave　motion　of　the　free　field　in　a　layered　half　space　proposed　by　Liu　and　Wang,　formulas　of　an　explicit　time-stepping　method　to　solve　the　out-of-plane　wave　motion　of　the　free　field　in　layered　media　with　damping　under　obliquely　incident　SH　wave　were　established　by　using　the　finite　difference　method,　and　its　numerical　program　was　developed　with　Fortran　programming　language.　A　cases　study　of　out-of-plane　wave　motions　of　the　free　field　in　one-layer　soil　and　two-layer　soil　with　damping　under　obliquely　incident　SH　wave　were　carried　out　respectively.　The　results　show　that:　soil　damping　only　has　effect　on　the　peak　displacements　of　free　field　motions,　and　has　no　effect　on　the　waveforms　of　the　displacement　time　histories;　the　displacement　amplitudes　in　layered　soil　with　damping　reduce　significantly　compared　with　that　of　without　damping　under　obliquely　incident　SH　wave,　and　the　displacement　amplitudes　can　be　reduced　by　40.5%　and　39.7%　for　one-layer　soil　and　two-layer　soil,　respectively.　The　case　study　also　indicates　that　the　attenuation　of　displacement　amplitudes　in　layered　soil　with　damping　gradually　increased　from　the　bottom　boundary　to　the　free　surface.　©　2017,　Editorial　Office　of　Journal　of　Vibration　and　Shock.　All　right　reserved.