The　numerical　manifold　method　(NMM)　is　characterized　by　its　two　cover　systems,　the　mathematical　cover　and　the　physical　cover.　In　the　standard　NMM,　the　mathematical　cover　is　required　to　cover　the　whole　problem　domain.　In　this　study,　however,　around　each　crack　tip　we　specify　a　small　domain　on　which　the　displacement　is　taken　as　the　truncated　Williams＇　displacement　series.　And　accordingly　all　such　small　domains　are　not　covered　by　the　mathematical　cover　that　only　covers　the　rest　of　the　problem　domain.　Meanwhile,　the　mathematical　cover　is　constructed　by　designating　all　supports　of　the　scattered　nodes　arising　in　the　moving　least　squares　interpolation　as　the　mathematical　patches.　In　this　way,　any　physical　patch　contains　no　crack　tip　and　can　be　approximated　by　polynomials.　As　a　result,　no　blending　element　issue　exists　as　in　the　extended　finite　element　method　and　NMM.　In　addition　to　high　precision,　the　proposed　procedure　is　especially　suitable　for　the　situation　where　a　crack　tip　is　very　close　to　other　cracks,　a　case　difficult　to　treat　by　the　interaction　integral　procedure　that　is　commonly　used　in　the　extraction　of　the　stress　intensity　factors　of　mixed　mode　cracks.