Accurately　simulating　the　dynamic　propagation　of　cracks　is　critical　to　investigating　the　mechanisms　of　rock　fracture　under　dynamic　loading.　The　meshless　numerical　manifold　method,　characterized　by　its　node-based　interpolation　approximation　akin　to　the　meshless　method　and　the　dual-cover　of　numerical　manifold　method,　is　particularly　suitable　for　crack　analysis　and　has　been　successfully　applied　to　quasi-static　crack　propagation.　This　paper　aims　to　extend　its　application　to　the　simulation　of　dynamic　crack　propagation.　Initially,　the　meshless　numerical　manifold　method＇s　nodal　arrangement　and　numerical　integration　scheme　are　enhanced　to　address　dynamic　problems　more　effectively,　referred　to　as　the　Improved　Meshless　Numerical　Manifold　Method　(iMNMM).　Subsequently,　we　introduce　a　novel　mass　lumping　method　grounded　in　rigorous　mathematical　principles,　an　energy-conserving　extended　degrees　of　freedom　inheritance　strategy　and　a　crack　propagation　criterion　based　on　dynamic　stress　intensity　factors.　Additionally,　the　viscous　artificial　boundaries　and　the　“large　mass”　acceleration　method　are　incorporated　to　impose　the　acceleration　and　zero-displacement　boundary　conditions.　Further,　the　improved　explicit　meshless　numerical　manifold　method　based　on　the　central　difference　method　is　established　for　dynamic　crack　propagation.　Finally,　for　verification,　iMNMM　is　tested　on　several　numerical　examples.　Numerical　results　manifest　that　iMNMM　can　enable　the　simulation　of　dynamic　crack　propagation　with　larger,　constant　time　steps.　©　2024　Elsevier　Ltd