This　research　addresses　the　free　vibration　performance　of　bi-directional　functionally　graded　materials　(BDFGMs)　rectangular　plate　with　general　boundary　restraints　and　geometrical　imperfections.　The　symmetric/asymmetric　material　distributions　subject　to　power-law　along　in-plane　two　directions　are　considered.　Two　types　of　geometric　imperfections　are　formulated　employing　transcendental　functions,　including　the　sine-type　imperfection　which　is　global　eccentric/symmetrical　and　depicted　by　sine　and　exponential　functions,　and　the　cosine-type　global/localized　imperfections　which　is　simulated　by　hyperbolic　and　cosine　functions.　The　general　boundary　restraints　are　imitated　by　artificial　virtual　springs.　The　Lagrangian　energy　function　is　formulated,　and　then　vibration　characteristics　of　plates　are　acquired　with　the　Ritz　method　and　improved　Fourier　series.　Verifications　are　carried　out　for　accuracy　of　theoretical　model　and　reliability　of　solution　method.　A　comprehensive　numerical　investigation　are　exhibited　to　explore　the　influencing　mechanism　of　material　distribution　patterns,　geometrical　imperfection　modal　and　elastic　boundary　restraints　on　vibration　performance　of　rectangular　plates.　The　results　show　that　the　in-plane　material　gradient　can　function　as　regulatory　measures　for　dynamic　characteristic　of　plates.　In　addition,　geometric　imperfections　may　cause　singularity　in　vibration　performance　of　plate.　These　innovative　results　may　serve　as　a　benchmark　for　future　studies　on　design　or　analysis　of　plates.　©　2022　Elsevier　Masson　SAS