Based　on　linear　three-dimensional　elasticity　theory,　the　wave　equations　of　coupled　Lamb　waves　in　multilayered　arbitrary　anisotropic　composite　laminates　are　derived　using　a　Legendre　orthogonal　polynomial　approach.　The　elastodynamic　solution　for　the　propagation　of　coupled　Lamb　waves　in　composite　plates　is　also　presented　to　determine　the　characteristics　of　coupled　Lamb　waves.　To　verify　the　applicability　and　validity　of　the　method,　two　cases　of　bi-layered　plates　formed　with　isotropic　components　and　anisotropic　components,　respectively,　are　primarily　manipulated　for　comparison　with　earlier　known　results.　Next,　the　dispersion　curves,　displacements　and　stress　distributions　of　Lamb　waves　in　multilayered　anisotropic　laminates　are　calculated.　The　effects　of　coupling　and　fiber　orientation　on　the　characteristics　of　the　Lamb　waves　are　illustrated.　The　potential　usefulness　of　the　fundamental　modes　of　the　coupled　Lamb　waves　is　discussed　in　detail.　(C)　2013　Elsevier　Ltd.　All　rights　reserved.