In　seepage　calculation　of　hydraulic　engineering,　there　are　a　large　number　of　singularity　problems　at　turning　point.　It　is　inconvenience　that　the　general　finite　element　method　needs　to　construct　special　singularity　shape　function　and　element　property　to　deal　with　the　singularity　problem,　which　used　to　be　ignored　when　the　isoparametric　element　was　widely　used.　In　this　paper,　a　new　method　by　constructing　a　local　special　patch　is　proposed　to　solve　this　singularity　problem　by　using　numerical　manifold　method.　Firstly,　the　singularity　covering　function　is　formed　together　by　the　constant　term　basis　function　and　a　new　basis　function　constructed　by　the　analytic　solution　at　turning　point.　The　singularity　covering　function　is　used　on　the　star　points　affected　by　the　singularity　point,　at　the　same　time,　the　constant　patch　covering　function　is　used　on　the　other　star　points,　and　the　calculation　result　approximates　the　real　solution　and　can　well　reflect　the　strong　singularity　in　the　corner.　Secondly,　the　discrete　formula　of　the　numerical　manifold　method　about　this　kind　of　problem　is　given,　and　the　classical　regular　triangle　of　manifold　element　is　improved　to　square,　as　well　as,　the　procedure　of　the　program　and　the　application　method　of　the　special　physical　patch　are　introduced.　Thirdly,　three　engineering　examples　are　respectively　confined　seepage　of　dam　foundation　with　impervious　curtain　contrast　with　the　analystic　solution,　the　comparison　of　the　classical　flow　velocity　drop　test,　and　the　confined　seepage　of　weir　with　sheet　pile　compared　with　flow　net　which　had　been　calculated,　those　show　the　effectiveness　and　correctness　of　the　method,　and　provide　a　basis　for　further　analysis　of　the　effects　of　singularity　on　the　structure　and　complex　engineering.　Finally,　The　proposed　method　is　also　applicable　to　other　numerical　analysis　methods　based　on　the　partition　of　unity　method　of　interpolation,　and　also　provides　an　approach　for　those　problems　with　continuous　field　and　discontinuous　partial　derivatives.　©　2017,　Science　Press.　All　right　reserved.