The　formulation　for　the　wave　propagation　in　a　multilayered　structure　with　an　anisotropic　layer　is　very　complex,　which　results　from　the　diversity　of　interfaces　and　the　specifieness　of　physical　properties　of　anisotropic　medium.　To　solve　this　issue,　based　on　the　transfer　matrix　method,　the　expressions　of　reflection　and　transmission　coefficients　for　SV　wave　and　SH　wave　of　the　lowest-order　mode　(SH0)　are　deduced　under　the　assumption　of　rigid　connection,　considering　a　three-layer　structure　with　only　orthotropic　middle　layer.　The　influences　of　incident　angle,　product　of　frequency-thickness　and　medium　of　intermediate　layer　on　the　shear　wave　propagation　characteristics　are　investigated　by　using　numerical　simulation　method.　The　results　show　that　the　critical　angle　will　appear　if　SV　wave　is　incident　into　a　multilayered　structure,　but　it　is　not　the　case　of　SH　wave.　When　the　sound　is　vertical　incidence,　with　the　increase　of　the　product　of　frequency-thickness,　the　phenomenon　of　the　multi-order　resonance　will　occur　with　respect　to　the　curves　of　reflection　and　transmission　coefficients　for　SV　wave　and　SH　wave.　The　results　provide　a　theoretical　basis　for　the　experimental　detection　of　multilayered　structure　which　is　similar　to　the　isotropic/orthotropic/isotropic　case　by　shear　waves.　©　2017,　The　Editorial　Board　of　Journal　of　Basic　Science　and　Engineering.　All　right　reserved.