The　present　study　investigated　the　coupling　effects　of　cracking　and　wave　propagation　on　the　underground　rock　mass　by　the　numerical　manifold　method　(NMM).　The　traditional　NMM　was　developed　for　the　simulation　of　dynamic　cracking　behavior　of　rock　mass.　One-dimensional　wave　propagation　was　utilized　to　validate　the　present　code.　Subsequently,　the　transient　stress　field　in　the　rock　mass　with　an　inclined　crack　was　investigated.　Finally,　two　cases　of　underground　caverns　with　symmetrical　or　unsymmetrical　discontinuities　under　stress　wave　were　simulated　to　validate　the　application　potentials.　The　results　show　that　the　transient　stress　field　is　not　only　influenced　by　the　stress　concentration　around　the　pre-existing　crack,　but　also　influenced　by　the　characteristics　of　stress　wave,　e.g.　reflection,　transmission　and　diffraction,　which　are　different　from　the　static　situation.　The　results　also　show　that　the　cracking　significantly　affects　the　stress　wave　duration　and　amplitude.　On　the　other　hand,　the　stress　wave　induced　cracking　depends　on　the　wave　propagation　distance　significantly.　Moreover,　the　NMM　can　be　used　to　simulate　the　cracking　behavior　of　underground　rock　mass　under　stress　wave　efficiently.