Aiming　to　solve,　in　a　unified　way,　continuous　and　discontinuous　problems　in　geotechnical　engineering,　the　numerical　manifold　method　introduces　two　covers,　namely,　the　mathematical　cover　and　the　physical　cover.　In　order　to　reach　the　goal,　some　issues　in　the　simulation　of　crack　propagation　have　to　be　solved,　among　which　are　the　four　issues　to　be　treated　in　this　study:　(1)　to　reduce　the　rank　deficiency　induced　by　high　degree　polynomials　as　local　approximation,　a　new　variational　principle　is　formulated,　which　suppresses　the　gradient-dependent　DOFs;　(2)　to　evaluate　the　integrals　with　singularity　of　1/r,　a　new　numerical　quadrature　scheme　is　developed,　which　is　simpler　but　more　efficient　than　the　existing　Duffy　transformation;　(3)　to　analyze　kinked　cracks,　a　sign　convention　for　argument　in　the　polar　system　at　the　crack　tip　is　specified,　which　leads　to　more　accurate　results　in　a　simpler　way　than　the　existing　mapping　technique;　and　(4)　to　demonstrate　the　mesh　independency　of　numerical　manifold　method　in　handling　strong　singularity,　a　mesh　deployment　scheme　is　advised,　which　can　reproduce　all　singular　locations　of　the　crack　with　regard　to　the　mesh.　Corresponding　to　the　four　issues,　typical　examples　are　given　to　demonstrate　the　effectiveness　of　the　proposed　schemes.　Copyright　(c)　2013　John　Wiley　&　Sons,　Ltd.