In　this　article,　we　investigate　the　effect　of　surface　tension　in　the　Rayleigh–Taylor　(RT)　problem　of　stratified　incompressible　viscoelastic　fluids.　We　prove　that　there　exists　an　unstable　solution　to　the　linearized　stratified　RT　problem　with　a　largest　growth　rate　Λ　under　the　instability　condition　(i.e.,　the　surface　tension　coefficient　ϑ　is　less　than　a　threshold　ϑc).　Moreover,　for　this　instability　condition,　the　largest　growth　rate　Λϑ　decreases　from　a　positive　constant　to　0,　when　ϑ　increases　from　0　to　ϑc,　which　mathematically　verifies　that　the　internal　surface　tension　can　constrain　the　growth　of　the　RT　instability　during　the　linear　stage.　©　2019,　The　Author(s).