This　study　presents　a　theoretical　approach　to　characterize　the　mesoscopic　dynamic　fracture　behaviors　of　concrete.　Firstly,　different　fracture　behaviors　are　determined　from　energy　criteria.　Secondly,　by　considering　the　energy　equivalence　principle,　the　Saint-Venant＇s　principle　and　the　Newton＇s　laws　of　motion,　an　extended　self-consistent　finite　stress　model　(XSFSM)　is　established　for　dynamic　fracture　analysis　of　concrete-like　cementitious　materials.　The　XSFSM　is　validated　and　modified　by　comparing　with　the　existing　models　in　design　codes　and　the　curve　fitting　models　in　literatures.　Thirdly,　the　XSFSM　is　utilized　to　propose　the　meso-level　fracture　criterion　of　concrete　based　on　a　morphological　material　model.　Parametric　study　illustrates　that　the　criterion　can　predict　the　transgranular　and　intergranular　failure　modes　of　concrete　under　quasi-static　to　dynamic　loading.　At　last,　assumptions　and　limitations　of　the　present　theoretical　approach　and　its　prospects　in　computational　methods　are　discussed.