Compared　with　the　finite　element　method,　H2-regularity　in　the　Galerkin　based　approximation　to　the　Kirchhoff　thin　plate　model　can　be　easily　realized　using　either　the　moving　least　squares　(MLS)　or　the　generalized　moving　least　squares　(GMLS),　which　take　the　Lagrange　form　and　the　Hermite　form,　respectively.　Coupling　(G)MLS　with　the　numerical　manifold　method　(NMM)　can　greatly　improve　numerical　properties　of　NMM　in　the　treatment　of　plates　of　complicated　shape,　thereby　denoted　by　MLS-NMM　and　GMLS-NMM.　In　the　(G)MLS-NMM,　the　mathematical　cover　is　composed　of　simply　connected　and　partially　overlapped　mathematical　patches　that　are　the　influence　domains　of　(G)MLS　nodes.　GMLS-NMM　appears　to　better　fit　to　the　Kirchhoff　plate　because　it　is　equipped　with　rotation　angle　degrees　of　freedom.　Through　numerical　tests　and　theoretical　analysis　in　solving　problems　of　thin　plates　on　elastic　foundations,　however,　this　study　shows　that　MLS-NMM　is　much　more　advantageous　over　GMLS-NMM　from　the　aspects　of　both　accuracy　and　memory　usage.　©　2023　Elsevier　Ltd