In　this　research,　based　on　the　weak　nonlinear　elasticity　theory　and　finite　deformation　theory,　a　dynamic　equation　of　guided　waves　in　pre-stressed　plates　is　established.　Legendre　orthogonal　polynomials　expansion　method　is　employed　to　analytically　solve　wave　equations.　The　dispersion　curves　and　particle　trajectory　are　obtained　without　root-finding　algorithm.　The　solution　is　validated　by　comparing　with　the　superposition　of　partial　bulk　wave　method,　and　its　convergence　properties　are　analyzed.　The　effects　of　the　pre-stress　states　on　particle　trajectory　and　ellipticity　dispersion　curves　are　investigated.　Results　confirm　that　the　behavior　of　particle　trajectory　and　ellipticity　dispersion　depends　not　only　on　the　pre-stress　states　but　also　on　frequency　and　mode.　Next,　ellipticity　dispersion　curve　of　fundamental　Lamb　modes　with　various　stress　state　and　propagation　directions　are　calculated.　Finally,　the　sensitivity　of　ellipticity　as　an　indicator　of　stress　is　also　analyzed.　These　results　provide　useful　reference　for　the　development　of　innovative　nondestructive　testing　method　for　pre-stress　states　based　on　Lamb　waves.