A　time-domain　artificial　boundary　condition　(ABC)　is　proposed　to　simulate　the　in-plane　vector　wave　in　a　linear　elastic　multilayered　waveguide　with　Rayleigh　damping.　The　ABC　is　stable　and　can　be　seamlessly　coupled　with　the　finite　element　method.　First,　the　vector　wave　equations　of　the　multilayered　waveguide　are　simplified　to　two　scalar　wave　equations,　which　are　decoupled　in　both　x　and　y　directions.　Then,　based　on　the　scaled　boundary　finite　element　method,　semi-discrete　frequency-domain　dynamic　stiffness　in　the　modal　space　is　obtained.　The　dynamic　stiffness　can　be　approximately　expressed　as　matrix　continued　fraction.　Finally,　the　continued　fraction　is　converted　to　the　time-domain　ABC　by　introducing　the　auxiliary　variable　technique.　In　this　method,　the　parameters　affecting　the　calculation　accuracy　and　efficiency　include　the　mode　number　n,　the　order　J　of　continued　fraction,　and　the　distance　L　from　the　artificial　boundary　to　the　region　of　interest.　Numerical　examples　show　that　only　the　mode　numbers　of　the　infinite　domain　excited　by　the　load　have　to　be　used.　J=3　can　be　taken　generally.　The　value　of　L　is　independent　of　the　size　of　the　underground　structure.　But　it　is　proportional　to　the　total　height　H　of　the　soil　layer,　and　the　relation　coefficient　is　related　to　the　material　parameters　of　the　soil　layer.　©　2021,　Chinese　Journal　of　Theoretical　and　Applied　Mechanics　Press.　All　right　reserved.