The　propagation　characteristics　of　elastic　wave　in　the　functional　graded　rectangular　bars　are　studied　by　the　two　dimensional　Rayleigh-Ritz　method.　Legendre　orthogonal　polynomials　are　used　as　trial　functions.　The　material　properties　are　assumed　to　be　graded　along　the　width　direction.　This　dispersion　equation　is　obtained　from　the　3D　variational　formulation　governing　elastodynamics.　The　convergence　and　accuracy　are　demonstrated　by　comparisons　with　the　available　solution　of　the　scaled　boundary　finite　element　method.　Finally,　we　give　some　phase　and　group　curves　of　various　rectangle　waveguides　and　analyze　influences　of　the　width　to　length　ratio　and　volume　fraction　indexes　on　dispersive　behavior　for　wave　propagation.　(C)　2015　Elsevier　Ltd.　All　rights　reserved.