The　sensitivity　of　vibration　characteristics　to　geometric　imperfection　in　rectangular　plates　made　with　FGMs　under　action　of　classic　or　elastic　constraints　is　studied.　It　is　assumed　that　the　material　changes　in　length　and　width　directions　of　plate.　The　energy　functions　of　plate　are　deduced　and　vibration　modals　are　solved　by　means　of　Ritz　procedure　along　with　the　modified　Fourier　series.　The　impacts　of　geometric　imperfection,　gradient　material　and　edge　conditions　on　vibration　features　of　rectangular　plates　are　simulated.　Numerical　results　demonstrate　that　material　gradient　could　be　considered　as　control　mechanism　for　dynamic　freatures　of　plate.　Moreover,　the　existence　of　geometric　imperfections　will　lead　singularity　of　vibration　characteristics　of　plate.　The　imperfection　sensitivity　of　vibration　behavior　in　plate　may　provide　important　reference　in　the　design　or　analysis　of　plates.　　©　Published　under　licence　by　IOP　Publishing　Ltd.