The　reflection　and　transmission　of　elastic　wave　in　a　multilayered　structure　composed　of　elastic　base　covered　with　magneto-electro-elastic　materials　were　fully　investigated.　With　the　general　Christoffel　equations,　the　expressions　of　general　displacements　(including　elastic　displacements,　electric　and　magnetic　potentials)　and　general　stresses　(including　stress,　electric　displacement　and　magnetic　induction)　were　derived.　Based　on　continuous　conditions　of　general　displacements　and　stresses　at　interfaces　of　adjacent　layers　and　given　boundary　conditions,　the　reflection　and　transmission　coefficients　of　elastic　wave　were　obtained　by　virtue　of　partial　wave　method　and　propagator　matrix　method.　As　numerical　example,　a　purely　elastic　multilayered　structure　was　used　to　verify　our　formulations.　Finally,　the　analysis　of　reflection　and　transmission　coefficients　of　wave　propagation　in　magneto-electro-elastic　multilayered　structure　were　realized,　which　also　showed　the　influences　of　different　incident　angle,　frequency　and　boundary　conditions　on　these　coefficients.