With　the　aid　of　an　efficient　meshless　numerical　solution　and　the　reproducing　kernel　particle　method,　the　feasibility　for　investigating　the　nonlinear　vibrations　of　the　carbon　fiber　reinforced　composite　rectangular　plate　with　the　random　material　properties　is　studied　in　this　paper.　A　geometrically　nonlinear　mathematical　model　is　established　based　on　the　classical　plate　theory.　According　to　the　derived　governing　equation　of　motion　by　using　the　principle　of　virtual　displacement,　the　nonlinear　vibration　behaviors　of　the　carbon　fiber　reinforced　composite　plates　with　various　edge　supports　are　investigated.　The　linear　and　nonlinear　eigenvalues　and　corresponding　eigenvectors　are　calculated　iteratively　by　using　the　dimensionless　amplitude.　The　stochastic　meshless　method　is　proved　to　have　a　good　computational　accuracy　for　the　composite　plate,　and　exhibits　an　optimal　choice　for　the　shape　function　and　constraint　of　the　essential　boundary　conditions.　The　useful　conclusions　are　obtained　regarding　the　effect　of　the　material　and　geometrical　parameters　including　the　boundary　condition,　length-width　ratio,　plate　length　and　carbon　fiber　content　on　the　nonlinear　responses　in　the　framework　of　the　meshless　method.　(c)　2020　Elsevier　Masson　SAS.　All　rights　reserved.