Based　on　the　linear　three-dimensional　elasticity　theory　and　＇Incremental　Deformation　Mechanics＇　theory,　the　wave　equations　of　acoustoelastic　Lamb　waves　propagating　along　the　non-principal　symmetry　axes　direction　of　fiber　reinforced　composite　lamina　were　derived　by　using　Legendre　orthogonal　polynomial　expansion　method　when　the　initial　stresses　were　applied　horizontally　and　vertically.　The　wave　equations　were　solved　numerically.　In　order　to　verify　the　accuracy　of　the　method,　the　dispersion　curves　of　phase　velocity　for　isotropic　material　obtained　by　the　author＇s　method　were　compared　with　that　from　＇Disperse®＇.　The　stress　distributions　of　wave　structure　without　initial　stress　were　computed　and　compared　with　the　initial　condition　of　stress　free　boundary　by　taking　a　fiber　reinforced　composite　lamina　as　an　example.　The　effects　of　horizontal　and　vertical　initial　stresses　on　the　dispersion　curves　of　Lamb　waves　were　studied.　Because　the　Lamb　wave　A0　mode　was　more　sensitive　to　the　acoustoelastic　effect,　the　influence　of　initial　stresses　on　the　displacement　distributions　of　wave　structure　was　investigated.　©　2020,　Engineering　Mechanics　Press.　All　right　reserved.