In　the　present　work,　the　phase　field　method　implemented　by　the　user-defined　element　(UEL)　subroutine　of　commercial　finite　element　software　ABAQUS　is　adopted　to　investigate　the　failure　pattern　and　mechanical　re-sponses　of　meso-scale　concrete　specimens.　To　build　the　structure　model　of　meso-scale　concrete　specimens,　the　recently　proposed　random　sequential　addition　(RSA)　method　is　used.　With　the　proposed　numerical　model,　the　uniaxial　tensile　test　was　carried　out　as　a　benchmark　test　to　investigate　the　influence　of　several　parameters,　such　as　the　volume　fraction,　size,　and　major　axis　direction　of　aggregates　on　the　mechanical　responses　and　failure　mode　of　concrete　specimens.　Then,　two　classic　examples,　namely,　a　three-point　bending　(TPB)　test　and　a　four-point　bending　(FPB)　test,　are　investigated　with　the　proposed　numerical　model.　The　numerical　results　from　the　pro-posed　numerical　model　indicate　that:　A　higher　interfacial　transition　zone　(ITZ)　content　has　an　adverse　effect　on　the　peak　strength　of　concrete;　A　negative　correlation　is　shown　between　major　axis　direction　of　aggregates　and　peak　strength　of　concrete;　Intergranular　fracture　mode　is　observed,　in　which　the　damage　areas　of　concrete　are　mainly　distributed　around　the　ITZ;　The　linear　elastic　stiffness　and　peak　strength　are　almost　independent　of　the　aggregate　distribution,　but　the　fracture　propagation　patterns　are　sensitive　to　meso-structures　of　concrete;　and　numerical　results　of　TPB　and　FPB　tests　also　indicate　that　the　notch　of　concrete　has　non-negligible　influences　on　fracture　propagation　path,　as　well　as　linear　elastic　stiffness　and　peak　load　of　concrete　specimens.