The　numerical　approach　is　a　vital　means　for　evaluating　the　stability　of　flawed　rocks.　In　this　paper,　the　extended　non-ordinary　state-based　peridynamics　(NOSB-PD)　theory　is　employed　to　simulate　the　fracture　process　of　rocks　containing　two　pre-existing　flaws.　Two　stress　criteria,　including　the　maximum　tensile　stress　criterion　and　the　Mohr-Coulomb　criterion,　are　implemented　into　the　NOSB-PD　numerical　method　to　respectively　judge　the　tensile　and　shear　failure　of　rock　materials.　The　effects　of　inclination　angles　and　ligament　angles　on　the　crack　initiation　and　coalescence　modes　for　flawed　rocks　are　investigated　based　on　the　numerical　results.　The　numerical　results　are　in　good　agreement　with　the　previous　experimental　results.　The　fracture　mechanism　of　flawed　rocks　is　revealed　based　on　the　evolutionary　distribution　characteristics　of　the　maximum　principal　stress　field　and　shear　stress　field　obtained　by　the　extended　NOSB-PD　theory.