A　modified　smoothed　particle　hydrodynamics　(SPH)　method　is　applied　to　simulate　the　dynamic　tensile　failure　of　rock-like　heterogeneous　materials.　The　material　heterogeneities　are　represented　by　different　mechanical　properties　with　a　Weibull　distribution　at　different　particles　over　the　specimen.　An　elasto-plastic-damage　model　is　adopted　to　simulate　material　failure.　Numerical　simulations　are　performed　for　three　specimens　with　different　degrees　of　heterogeneity　under　quasi-static　and　dynamic　loading　conditions,　respectively.　The　effects　of　strength　criterion　coefficient　b　on　the　predicted　tensile　strength　are　also　discussed.　Results　show　that　the　material　heterogeneity　has　significant　effect　on　the　dynamic　tensile　failure,　especially　at　a　higher　strain　rate　loading　condition.　At　a　lower　strain　rate,　the　failure　mode　of　heterogeneous　material　is　very　much　similar　to　that　of　homogeneous　materials.　At　a　higher　strain　rate,　plenty　of　micro　cracks　occur　forming　a　failure　band　in　the　tension　zones.　Moreover,　the　value　of　strength　criterion　coefficient　b　has　a　considerable　influence　on　the　tensile　strength　under　a　higher　loading　rate.