In　order　to　solve　problems,　from　a　continuum　point　of　view　and　in　a　unified　way,　involving　continuum　and　discontinuum　deformation,　and　small　deformation　and　large　movement,　the　numerical　manifold　method　(NMM)　introduces　two　covers,　namely　the　mathematical　cover　(MC)　and　the　physical　cover　(PC).　This　study　generates　the　MC　with　the　influence　domains　of　nodes　in　the　moving　least　squares　(MLS)　interpolation　instead　of　commonly-used　finite　element　meshes,　significantly　simplifying　the　generation　of　PCs　and　the　simulation　of　crack　growth.　Advantageous　over　the　conventional　meshfree　method,　the　MLS-based　NMM　can　naturally　treat　complex　geometry　without　recourse　to　those　complicated　but　contrived　criteria　or　operations.　Moreover,　the　treatment　of　large　movement　caused　by　cracking　is　much　easier　with　the　MLS-based　NMM　than　with　the　FE-based　NMM.