The　nonlinearity　of　macro-mechanical　properties　and　the　size　effect　of　concrete　are　mainly　caused　by　its　heterogeneity.　Considering　the　mesoscopic　heterogeneity,　meso-mechanical　models　were　set　up,　which　were　composed　of　the　aggregates,　mortar　matrix　and　interfacial　transition　zones　(ITZ).　The　damage　process　of　concrete　cubic　specimens　subjected　to　splitting　tensile　loading　was　simulated,　with　cube　side　lengths　including　150　mm,　250　mm,　350　mm　and　450　mm.　The　effect　of　aggregate　sizes　(10　mm,　20　mm,　30　mm　and　40　mm)　on　the　mechanical　properties　and　specimen　size　effect　was　studied.　The　simulated　results　were　compared　with　test　data.　It　was　shown　that　the　splitting　tensile　strength　decreases　slightly　with　an　increase　in　aggregate　size,　however,　once　the　aggregate　size　is　increased　to　30mm,　this　decline　slows.　There　exists　a　size　effect　on　splitting　tensile　strength　for　cubic　specimens　with　different　aggregate　sizes.　The　specimens　with　small-sized　aggregates　become　more　brittle　in　the　damage　process　than　the　specimens　with　big-sized　aggregates.　Therefore　the　size　effect　of　specimens　with　small-sized　aggregates　is　more　obvious.　The　simulation　data　fit　well　with　the　size　effect　law　proposed　by　Baant　and　Weibull.　©　2017,　Engineering　Mechanics　Press.　All　right　reserved.