Site　response　analysis　is　an　important　topic　in　earthquake　engineering.　A　time-domain　numerical　method　called　as　one-dimensional　(1D)　finite　element　artificial　boundary　method　is　proposed　to　simulate　the　homogeneous　plane　elastic　wave　propagation　in　a　layered　half　space　subjected　to　the　obliquely　incident　plane　body　wave.　In　this　method,　an　exact　artificial　boundary　condition　combining　the　absorbing　boundary　condition　with　the　inputting　boundary　condition　is　developed　to　model　the　wave　absorption　and　input　effects　of　the　truncated　half　space　under　layer　system.　The　spatially　two-dimensional　(2D)　problem　consisting　of　the　layer　system　with　the　artificial　boundary　condition　is　transformed　equivalently　into　a　1D　one　along　the　vertical　direction　according　to　Snell＇s　law.　The　resulting　1D　problem　is　solved　by　the　finite　element　method　with　a　new　explicit　time　integration　algorithm.　The　1D　finite　element　artificial　boundary　method　is　verified　by　analyzing　two　engineering　sites　in　time　domain　and　by　comparing　with　the　frequency-domain　transfer　matrix　method　with　fast　Fourier　transform.