We　proposed　a　generalized　moving　least　squares　(GMLS)　based　numerical　manifold　method　(NMM)　and　applied　to　investigate　mechanical　behaviors　of　thin　plates　with　various　shape　and　cutouts.　The　influence　domains　of　nodes　in　generalized　moving　least　squares　(GMLS)　interpolation　are　employed　to　construct　the　mathematical　cover,　which　is　specifically　fitted　for　the　fourth-order　problems　with　rotational　degrees　of　freedom.　Moreover,　the　GMLS-based　NMM　can　naturally　treat　plates　with　arbitrary　complex　geometry　and　openings　without　resorting　to　those　complicated　criteria　and　tailored　operations　while　simplifying　the　physical　cover　generation　process.　In　numerical　study,　a　suitable　mass　lumping　scheme　is　formulated　and　advised　for　transverse　vibration　analysis.　Bending,　vibration　and　buckling　behaviors　of　thin　plates　with　different　shapes　and　cutouts　are　studied.　Numerical　results　manifest　that　GMLS-based　NMM　can　accurately　model　transverse　mechanical　behaviors.　©　2023　Elsevier　Ltd