The　wave　propagation　in　the　unbounded　domain　is　a　hottest　topic　in　engineering　research.　Based　on　the　scaled　boundary　finite　element　method,　an　efficient　and　accuracy　artificial　boundary　condition　is　proposed　for　the　wave　propagation　in　half　space,　and　the　shape　of　the　artificial　boundary　can　be　arbitrary,　such　as　ellipse　and　rectangle.　A　new　continued　fraction　for　solving　the　dynamic　stiffness　is　derived,　and　by　introducing　auxiliary　variables,　it　can　be　transformed　into　time　domain　conveniently.　The　dynamic　stiffness　of　the　artificial　boundary　condition　in　frequency　domain　in　good　agreement　with　the　exact　solution　in　high　frequencies.　The　circle　and　ellipse　artificial　boundary　condition　is　identical　with　the　reference　solution　in　time　domain.　©　Published　under　licence　by　IOP　Publishing　Ltd.