The　objectives　of　the　present　study　are　to　discover　the　influences　of　stirrup　ratio　and　shear-span　ratio　on　the　shear　failure　and　size　effect　of　reinforced　concrete　(RC)　beams　having　different　sizes,　and　to　build　a　theoretical　formula　for　quantitatively　describing　the　size　effect　on　shear　failure　of　RC　beams.　A　three-dimensional　meso-scale　simulation　method　for　modelling　the　failure　of　RC　beams　is　established,　and　it　is　utilized　to　explore　the　failure　behavior　of　geometrically-similar　RC　beams.　In　addition,　the　influences　of　shear-span　ratio　and　stirrup　ratio　on　the　size　effect　of　shear　failure　was　examined.　Finally,　a　novel　size　effect　law　(SEL)　for　predicting　the　nominal　shear　strength　of　RC　beams　having　different　sizes　is　established　and　verified.　The　results　indicate　that,　(1)　the　shear-span　ratio　has　a　great　influence　on　the　shear　capacity　of　RC　cantilever　beams,　but　has　ignorable　effect　on　the　size　effect;　(2)　the　increase　of　stirrup　ratio　increases　the　shear　capacity　of　RC　cantilever　beams　and　weakens　the　size　effect　of　the　shear　strength;　(3)　stirrups　cannot　increase　the　shear　capacity　of　RC　beams　indefinitely,　and　the　increase　of　shear　strength　is　obvious　under　the　condition　of　small　stirrup　ratio;　(4)　the　developed　SEL　for　shear　failure　of　RC　beams　can　well　describe　the　quantitative　influence　of　stirrup　ratio　and　shear-span　ratio,　and　it　is　consistent　with　the　available　test　date.