Although　great　progress　has　been　made　in　the　research　of　size　effect　laws　of　concrete　materials,　little　attention　has　been　paid　on　the　size　effect　theory　of　concrete-filled　steel　tube　components.　In　this　study,　a　three-dimensional　mesoscopic　numerical　analysis　model　is　established　to　explore　the　axial　compressive　failure　of　circular　concrete-filled　steel　tubular　columns,　considering　concrete　heterogeneity　and　interaction　between　the　steel　tube　and　concrete.　A　good　agreement　between　our　simulation　results　and　the　existing　experimental　results　is　achieved.　Also,　the　axial　compressive　failure　mechanism　and　failure　modes　of　concrete-filled　steel　tubular　columns　under　different　lateral　constraints　(represented　by　confinement　coefficients)　and　different　structural　sizes　are　studied　by　using　the　mesoscopic　simulation　method.　In　addition,　the　effect　of　horizontal　confinement　on　the　nominal　axial　compressive　strength　of　concrete　columns　and　the　corresponding　size　effect　are　revealed.　Finally,　by　applying　the　influencing　mechanism　of　steel　tube　to　the　axial　compressive　strength　of　concrete　columns,　causing　the　strength　enhancement　effect　and　size　effect　weakening　effect,　based　on　the　size　effect　law　of　material　level,　a　theoretical　formula　of　size　effect　reflecting　the　axial　compressive　strength　of　concrete　columns　under　lateral　constraint　is　established.　The　accuracy　and　rationality　of　the　derived　theoretical　formula　are　verified.　©　2020,　Science　Press.　All　right　reserved.