The　problem　of　frictional　discontinuities　in　rock　masses　is　addressed　computationally　in　the　context　of　the　NMM　(numerical　manifold　method).　The　use　of　the　NMM　allows　the　use　of　nonmatching　meshes　to　discretize　the　problem　domain.　To　impose　frictional　contact　conditions,　the　Uzawa-type　ALM　(augmented　Lagrange　method),　which　inherits　the　merits　of　the　LMM　(Lagrange　multiplier　method)　and　the　PM　(penalty　method),　is　incorporated　into　the　NMM,　and　a　numerical　model　termed　as　Uzawa-type　augmented　Lagrangian　numerical　manifold　method　(UALNMM)　is　proposed.　In　the　UALNMM,　two　layers　of　iterations　are　adopted,　which　are　NewtonRaphson　iterations　for　the　inner　layer　and　augmentation　iterations　for　the　outer　layer.　The　implementation　of　the　UALNMM　is　discussed　in　details.　Four　benchmark　examples　of　frictional/frictionless　contact　problems　and　an　example　of　rock　slope　with　multiple　frictional　fractures　are　used　to　validate　the　accuracy　and　robustness　of　the　UALNMM.　The　proposed　UALNMM　deserves　further　investigation　for　three　dimensional　rock　mechanics　problems　with　frictional　contact.