We　investigate　the　stabilizing　effect　of　elasticity　in　the　Rayleigh-Taylor　(RT)　problem　of　stratified　immiscible　viscoelastic　fluids,　separated　by　a　free　interface　and　in　the　presence　of　a　uniform　gravitational　field,　in　a　horizontally　periodic　domain　where　the　velocities　of　the　fluids　are　non　-slip　on　both　upper　and　lower　fixed　flat　boundaries,　while　the　internal　surface　tension　is　omitted.　We　establish　a　discriminant　Cr　for　the　stability　of　the　stratified　viscoelastic　RT　problem.　More　precisely,　if　Cr　＜　1,　then　the　stratified　viscoelastic　RT　equilibrium　state　is　exponentially　stable.　This　means　that　a　sufficiently　large　elasticity　coefficient　has　stabilizing　effect　so　that　it　can　inhibit　viscoelastic　RT　instability.　On　the　other　hand,　if　Cr　＞　1,　then　we　show　that　the　RT　equilibrium　state　is　linearly　unstable　in　the　Hadaroard　sense.　Moreover,　for　the　case　of　a　nonhomogeneous　incompressible　viscoelastic　fluid,　the　condition　Cr　＞　1　will　lead　to　the　nonlinear　instability　of　the　RT　equilibrium　state;　and　this　shows　that　the　RT　instability　still　occurs　in　viscoelastic　fluids　when　the　elasticity　coefficient　is　small.　(C)　2017　Elsevier　Inc.　All　rights　reserved.