To　simulate　the　entire　process　of　the　progressive　failure　of　rock　slopes,　a　series　of　techniques　are　incorporated　into　the　original　NMM　(numerical　manifold　method).　To　reflect　the　stress　concentration　near　the　crack　tip,　the　Williams＇　displacement　series　is　adopted　to　enrich　the　global　displacement　function　of　the　NMM.　Furthermore,　the　most　recently　proposed　strength-based　LT　criterion,　which　can　account　for　tensile　cracks,　tensile-shear　cracks　and　compressive-shear　cracks,　is　adopted　to　determine　the　crack　propagation　direction　and　length.　Three　typical　numerical　examples,　including　a　Mode-I　crack　problem,　a　Mode-II　crack　problem　and　a　Brazilian　disc　problem　are　adopted　to　verify　the　numerical　model.　The　numerical　results　indicate　that　the　numerical　model　is　capable　of　accurately　simulating　the　Mode-I　crack　propagation　problem,　the　mode-II　crack　propagation　problem　and　the　failure　process　of　Brazilian　disc.　Furthermore,　the　numerical　model　is　adopted　to　investigate　the　entire　progressive　failure　process　of　two　rock　slopes.　The　corresponding　results　indicate　that　the　numerical　model　can　not　only　simulate　the　propagation　and　coalescence　of　multiple　cracks　in　rock　masses　but　also　the　opening/sliding　of　rock　blocks　along　discontinuities.　The　proposed　numerical　model　warrants　further　investigation.