This　paper　applies　the　GMLS-based　numerical　manifold　method　(NMM)　in　analyzing　the　buckling　behaviors　of　thin　plates.　The　numerical　manifold　method　(NMM),　deploying　two　cover　systems,　namely　the　mathematical　cover　(MC)　and　physical　cover　(PC),　has　been　successfully　employed　in　the　continuum　and　discontinuum　deformation　analysis.　In　this　study,　the　MC　system　is　constructed　with　influence　domains　in　generalized　moving　least　squares　(GMLS)　interpolation　rather　than　the　commonly-used　finite　element　meshes,　which　is　especially　fitted　for　the　fourth-order　problems　with　rotational　degrees　of　freedom　and　simplifies　the　possess　of　generating　physical　cover　system.　Moreover,　the　GMLS-based　NMM　can　be　readily　utilized　to　treat　plates　with　arbitrary　complex　geometry　and　openings　without　resorted　to　those　complicated　criteria　and　tailored　operations.　A　series　of　numerical　experiments　concerning　buckling　analysis　for　thin　plates　with　various　shapes　and　cutouts　have　been　performed,　thus　validating　the　effectiveness　and　accuracy　of　the　proposed　GMLS-based　numerical　manifold　method.