Given　the　significant　potential　of　multi-directional　functionally　graded　materials　(MFGMs)　for　customizable　performance,　it　is　crucial　to　develop　versatile　material　models　to　enhance　design　optimization　in　engineering　applications.　This　paper　introduces　a　material　model　for　an　MFGM　plate　described　by　trigonometric　functions,　equipped　with　four　parameters　to　control　diverse　material　distributions　effectively.　The　bending　and　vibration　analysis　of　MFGM　rectangular　and　cutout　plates　is　carried　out　utilizing　isogeometric　analysis,　which　is　based　on　a　novel　third-order　shear　deformation　theory　(TSDT)　to　account　for　transverse　shear　deformation.　The　present　TSDT,　founded　on　rigorous　kinematics　of　displacements,　is　demonstrated　to　surpass　other　preceding　theories.　It　is　derived　from　an　elasticity　formulation,　rather　than　relying　on　the　hypothesis　of　displacements.　The　effectiveness　of　the　proposed　method　is　verified　by　comparing　its　numerical　results　with　those　of　other　methods　reported　in　the　relevant　literature.　Numerical　results　indicate　that　the　structure,　boundary　conditions,　and　gradient　parameters　of　the　MFGM　plate　significantly　influence　its　deflection,　stress,　and　vibration　frequency.　As　the　periodic　parameter　exceeds　four,　the　model　complexity　increases,　causing　result　fluctuations.　Additionally,　MFGM　cutout　plates,　when　clamped　on　all　sides,　display　almost　identical　first　four　vibration　frequencies.