Considering　the　heterogeneity　and　strain-rate　effects　of　meso-components,　concrete　was　simulated　as　a　three-phase　composite　and　a　3D　meso-scale　numerical　method　was　set　up.　The　splitting　tensile　failure　of　315　concrete　cubic　samples　having　different　side　lengths　with　different　aggregate　contents　and　maximum　aggregate　sizes　(MAS)　has　been　explored　by　using　the　meso-scale　numerical　approach.　In　addition,　the　effect　of　aggregate　contents　and　MAS　on　dynamic　mechanical　properties　and　the　corresponding　dynamic　size　effect　of　concrete　was　analyzed.　The　simulation　results　indicate　that　the　size　effect　on　dynamic　splitting　tensile　strength　of　concrete　materials　is　closely　associated　with　the　applied　strain-rates.　Appropriate　enhancement　in　aggregate　contents　and　MAS　can　increase　the　nominal　strengths　of　concrete　under　different　strain-rates.　Aggregate　contents　and　MAS　present　obvious　influences　on　the　size　effect　of　splitting　tensile　strengths　under　low(er)　strain-rates　while　they　perform　little　effect　on　the　dynamic　size　effect　under　high(er)　strain-rates.　Furthermore,　the　developed　static　and　dynamic　unified　size　effect　law　(SD-SEL)　for　concrete　materials　can　quantitatively　predict　the　size　effect　on　dynamic　splitting　tensile　strength.