This　study　is　to　explore　the　influence　of　maximum　aggregate　size　(MAS)　on　the　failure　and　corresponding　size　effect　of　concrete　materials　under　low　strain　rates.　The　failure　process　of　concrete　was　simulated　by　the　meso-scale　numerical　method　considering　the　internal　heterogeneity　of　concrete　and　strain　rate　effect.　Based　on　the　meso-scale　method,　the　failure　behavior　of　concrete　specimens　with　different　structural　sizes　and　MAS　was　investigated.　Also,　the　influence　of　MAS　on　the　failure　modes,　nominal　strength　and　corresponding　size　effect　of　concrete　were　studied　at　the　meso-scale.　The　simulation　results　indicated　that　MAS　has　an　obvious　influence　on　the　failure　modes　of　concrete　subjected　to　axial　compressive　and　tensile　loads.　The　nominal　tensile　strength　increased　as　the　MAS　increased,　while　the　nominal　compressive　strength　increased　first　and　then　decreased　as　the　MAS　increases　under　quasi-static　load.　In　addition,　it　was　found　that　the　size　effect　on　nominal　strength　of　concrete　would　be　weakened　with　the　increase　of　strain　rate.　When　the　applied　strain　rate　reached　1　s-1,　the　size　effect　on　nominal　strength　of　concrete　disappeard.　Moreover,　the　MAS　has　an　ignorable　influence　on　the　dynamic　size　effect　of　concrete　under　uniaxial　compression　and　tension.　©　2020,　Editorial　Department　of　Transactions　of　NUAA.　All　right　reserved.