Due　to　its　dual　cover　systems　(i.e.,　the　mathematical　cover　and　the　physical　cover),　the　numerical　manifold　method　(NMM)　is　outstanding　in　crack　modeling,　especially　in　the　simulation　of　complex　cracks.　In　this　paper,　the　NMM　is　extended　to　calculate　the　T-stresses　for　two-dimensional　multiple-branched　and　intersecting　cracks.　The　displacement　jump　across　crack　surface　is　essentially　portrayed　by　the　NMM,　and　the　stress　singularity　at　the　crack　tip　is　represented　through　the　incorporation　of　related　asymptotic　basis　in　the　NMM　local　functions.　The　T-stresses　are　extracted　with　the　domain-form　interaction　integral　in　the　NMM　postprocessing.　To　validate　the　proposed　scheme,　three　numerical　examples　are　tested　on　uniform　mathematical　covers　nonconforming　with　all　domain　boundaries,　and　the　computed　results　are　in　nice　consistence　with　the　existing　solutions.　Besides,　the　effects　of　crack　configurations　and　boundary　conditions　on　the　T-stresses　are　also　revealed.