In　practical　engineering,　most　concrete　structures　are　in　complex　stress　states.　The　lateral　stress　ratio　presents　significant　influences　on　the　mechanical　properties　of　concrete　under　multiaxial　stress.　In　this　study,　a　3D　mesoscopic　modelling　approach　was　established　to　simulate　the　mechanical　behavior　of　concrete　specimens　having　different　sizes　under　quasi-static　biaxial　compression　(C-C　case)　and　biaxial　compression-tension　(C-T　case)　at　different　lateral　stress　ratios　lambda　(lambda　=　0,　+/-　0.25,　+/-　0.5,　+/-　0.75,　+/-　1,　and　infinity).　The　influences　of　the　lateral　stress　ratio　on　the　failure　mode,　the　nominal　spindle　compressive　strength,　nominal　lateral　tensile　strength　(only　under　C-T　case)　and　the　corresponding　size　effect　were　investigated.　The　results　indicate　that　the　spindle　compressive　strength　first　increases　and　then　decreases　for　the　C-C　case.　The　corresponding　size　effect　is　gradually　weakened　and　then　strengthened　as　the　lateral　stress　ratio　increases.　While　for　the　C-T　case,　with　the　increase　of　the　lateral　stress　ratio,　the　spindle　compressive　strength　gradually　decreases　and　the　corresponding　size　effect　gradually　increases.　Correspondingly,　the　lateral　tensile　strength　gradually　decreases　and　the　corresponding　size　effect　gradually　increases　by　the　increasing　spindle　compressive　stress.