Formulations　of　a　four-node　quadrilateral　element　fitted　to　numerical　manifold　method　(NMM)　with　continuous　nodal　stress　called　Quad4-CNS　(NMM)　element　for　two-dimensional　(2D)　crack　analysis　are　presented.　This　Quad4-CNS　(NMM)　element　can　be　considered　as　a　development　of　the　recently　published　four-node　quadrilateral　element　with　continuous　nodal　stress　(Quad4-CNS).　In　contrast　to　the　four　node　iso-parametric　quadrilateral　element　(Quad4),　the　Quad4-CNS　element　has　higher　order　of　global　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　(PU)　based　methods　with　high　order　global　approximations.　Due　to　the　adoption　of　two　cover　systems,　namely,　the　mathematical　cover　and　physical　cover,　the　NMM　is　capable　of　solving　continuous　and　discontinuous　problems　in　a　unified　way.　The　purpose　of　this　paper　is　to　synergize　the　advantages　of　both　the　Quad4-CNS　element　and　the　NMM　to　precisely　model　linear　elastic　fracture　problems.　A　number　of　numerical　examples　indicate　the　accuracy　and　robustness　of　the　present　Quad4-CNS　(NMM)　element.　(C)　2016　Elsevier　Ltd.　All　rights　reserved.