A　three-node　triangular　element　fitted　to　the　numerical　manifold　method　with　continuous　nodal　stress　called　Trig3-CNS　(NMM)　element　for　accurately　modeling　two-dimensional　linear　elastic　fracture　problems　is　presented.　By　adopting　two　cover　systems,　namely,　the　mathematical　cover　and　physical　cover,　the　numerical　manifold　method　(NMM)　could　easily　solve　continuous　and　discontinuous　problems　in　a　unified　way.　In　contrast　to　the　three-node　triangular　element　(Trig3),　the　Trig3-CNS　element　has　higher　order　of　approximations,　much　better　accuracy　and　continuous　nodal　stress.　Moreover,　it　is　free　from　the　＂linear　dependence＂　which　otherwise　cripples　many　of　the　partition　of　unity　based　methods　with　high　order　approximations.　The　purpose　of　the　present　work　is　to　synergize　the　advantages　of　both　the　recently　developed　Trig3-CNS　element　and　the　NMM　to　precisely　model　two-dimensional　linear　elastic　fracture　problems.　A　number　of　numerical　examples　indicate　the　accuracy　and　robustness　of　the　present　Trig3-CNS　(NMM)　element.　(C)　2016　Elsevier　Ltd.　All　rights　reserved.