This　paper　presents　a　theoretical　study　on　the　determination　of　intergranular　and　transgranular　failure　of　mesoscale　concrete　under　mode-I　fracture.　The　material　model　for　concrete　is　set　up　based　on　the　three　main　meso　structures,　i.e.　mortar,　interface　and　aggregate.　The　failure　of　concrete　is　characterized　by　its　morphological　fracture　features　in　direct　tension.　Concept　of　meso-level　fracture　criterion　is　proposed　based　on　the　mesoscale　model　concrete.　A　self-consistent　finite　stress　model　(SFSM)　for　concrete-like　cementitious　materials　is　established　and　the　meso-level　crack　path　criterion　of　concrete　is　presented　based　on　the　SFSM.　Two　kinds　of　determination　method　for　the　mesoscopic　fracture　index　are　presented.　The　probability　of　aggregate　fracture　is　formulated　based　on　the　variation　of　aggregate　fracture　index.　Moreover,　sensitivity　analysis　indicates　that,　the　main　factors　in　the　formulation　of　aggregate　fracture　index　should　receive　sufficient　attention　in　future　experimental　and　numerical　works.