The　traditional　numerical　manifold　method　(NMM)　adopts　the　form　of　regional　integration.　This　paper　proposed　a　new　NMM　in　the　form　of　boundary　integral　by　integrating　the　advantages　of　both　the　boundary　element　method　(BEM)　and　the　NMM,　namely　the　dimension　reduction　of　BEM　and　the　flexibility　of　local　base　selection　of　NMM.　For　two-dimensional　elastostatics　problems,　three　different　benchmark　examples　with　analytical　solutions　are　applied　to　verify　the　validity　and　efficiency　of　the　newly　proposed　NMM.　The　results　show　that　the　accuracy　of　the　proposed　procedure　can　be　effectively　improved　by　increasing　the　order　of　the　local　basis.　©　2020,　Science　Press.　All　right　reserved.