This　paper　presents　a　study　of　the　critical　angles　of　obliquely　incident　stress　wave　through　a　single　joint　with　different　mediums　on　both　sides.　Based　on　the　displacement　discontinuity　method　(DDM)　and　Snell＇s　law,　the　propagation　characteristics　of　obliquely　incident　stress　wave　through　the　joint　with　the　different　mediums　on　both　sides　are　investigated.　The　existence　of　critical　angles　is　judged,　and　the　reflection　and　transmission　of　the　stress　wave　before　and　after　the　critical　angles　are　analyzed.　The　effects　of　the　frequency　of　the　incident　wave,　joint　stiffness,　and　mechanical　properties　of　mediums　on　the　critical　angles　are　studied.　The　results　show　that　the　first　critical　angle　exists　in　the　cases　of　the　P　wave　velocity　of　medium　II　is　larger　than　that　of　medium　I,　and　both　the　first　and　second　critical　angles　exist　in　the　cases　of　the　S　wave　velocity　of　medium　II　are　larger　than　the　P　wave　velocity　of　medium　I.　The　first　and　second　critical　angles　are　only　affected　by　the　mechanical　properties　of　mediums,　and　not　affected　by　the　frequency　of　the　incident　wave　and　joint　stiffness.　Both　the　first　and　second　critical　angles　increase　as　the　density　of　medium　II　increases,　while　both　the　first　and　second　critical　angles　decrease　as　the　Young＇s　modulus　of　medium　II　increases.　It　is　noted　that　the　first　critical　angle　decreases　while　the　second　critical　angle　increases　as　the　Poisson＇s　ratio　of　medium　II　increases.