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　Lambda　under　the　instability　condition　(i.e.,　the　surface　tension　coefficient　v　is　less　than　a　threshold　v(c)).　Moreover,　for　this　instability　condition,　the　largest　growth　rate　Delta(v)　decreases　from　a　positive　constant　to　0,　when　v　increases　from　0　to　v(c),　which　mathematically　verifies　that　the　internal　surface　tension　can　constrain　the　growth　of　the　RT　instability　during　the　linear　stage.