To　simulate　the　moving　boundary　problems,　the　moving　least　square-based　numerical　manifold　method,　abbreviated　as　MLS-based　NMM,　was　proposed.　The　MLS-based　NMM　has　been　applied　successfully　to　open　crack　problems,　which　exhibits　the　high　accuracy　and　strong　robustness.　In　this　study,　we　extend　the　MLS-based　NMM　to　simulate　the　cracked　rock　considering　the　contact　of　the　crack　surface.　Simultaneously,　in　order　to　simulate　the　progressive　failure　of　the　cracked　rock,　an　improved　strength-based　criterion　is　proposed.　The　criterion　is　based　on　the　Mohr-Coulomb　criterion　and　maximum　tensile　stress　criterion.　Because　rock　can　be　regarded　as　a　quasi-brittle　material,　a　characteristic　distance　is　used　to　calculate　the　crack　tip　stress　and　correct　the　crack　propagation　direction　which　avoids　the　phenomenon　of　＂Zig-zag＂　for　the　crack　propagation　path　based　on　the　fracture　mechanics　criterion.　The　proposed　strength-based　criterion　can　acquire　the　crack　tip　stress　and　propagation　direction　and　also　realize　the　automatic　determination　of　the　crack　propagation　length　in　each　step　of　the　crack　growth.　A　Brazilian　disc　problem　and　a　rectangular　plate　problem　are　adopted　to　verify　the　numerical　model.　At　last,　the　numerical　model　is　applied　to　study　the　progressive　failure　process　of　the　rock　slope.　The　results　indicate　that　the　proposed　method　can　deal　with　the　crack　propagation　in　the　rock　and　the　opening/sliding　of　rock　blocks　along　discontinuities　in　a　natural　way.