In　the　numerical　manifold　method　(NMM),　the　mathematical　patches　composing　the　mathematical　cover　can　take　on　any　shape　in　addition　to　finite　elements.　In　this　study,　the　influence　domains　of　those　scattered　nodes　in　the　moving　least　squares　(MLS)　approximation　serve　as　the　mathematical　patches.　And　accordingly,　the　MLS　based　NMM,　designated　by　MLS-NMM,　is　derived,　which　owns　the　advantages　of　both　NMM　and　MLS.　Then,　MLS-NMM　is　applied　to　analyze　cracked　bodies　under　dynamic　loading,　and　a　mass　lumping　scheme　fit　for　MLS-NMM　is　proposed.　The　dynamic　analyses　of　some　typical　cracked　bodies　are　carried　out,　indicating　MLS-NMM　equipped　with　the　proposed　mass　lumping　scheme　has　more　excellent　numerical　properties　than　that　with　the　consistent　mass　formulation　in　the　analysis　of　the　time　domain　as　well　as　the　frequency　domain.　(C)　2017　Elsevier　Ltd.　All　rights　reserved.