A　modified　smoothed　particle　hydrodynamics　(SPH)　method　is　applied　to　simulate　the　failure　process　of　heterogeneous　materials.　An　elastoplastic　damage　model　based　on　an　extension　form　of　the　unified　twin　shear　strength　(UTSS)　criterion　is　adopted.　Polycrystalline　modeling　is　introduced　to　generate　the　artificial　microstructure　of　specimen　for　the　dynamic　simulation　of　Brazilian　splitting　test　and　uniaxial　compression　test.　The　strain　rate　effect　on　the　predicted　dynamic　tensile　and　compressive　strength　is　discussed.　The　final　failure　patterns　and　the　dynamic　strength　increments　demonstrate　good　agreements　with　experimental　results.　It　is　illustrated　that　the　polycrystalline　modeling　approach　combined　with　the　SPH　method　is　promising　to　simulate　more　complex　failure　process　of　heterogeneous　materials.