We　choose　a　constitutive　model,　which　consists　of　a　viscous　stress　component　and　a　stress　component　for　a　neo-Hookean　solid,　to　describe　the　motion　of　a　viscoelastic　fluid　heated　from　below,　and　then　mathematically　investigate　the　stability　for　the　Rayleigh-Benard　problem　of　the　constitutive　model.　A　stability　criterion　is　established,　under　which　the　Rayleigh-Benard　problem　is　exponentially　stable　with　respect　to　time.　Our　stability　result　shows　that　the　elasticity　can　inhibit　the　thermal　instability　under　sufficiently　large　elasticity　coefficient　.　In　addition,　we　also　provide　an　instability　criterion,　under　which　the　Rayleigh-Benard　problem　is　unstable.　Our　instability　result　shows　that　elasticity　can　not　inhibit　the　thermal　instability,　when　is　too　small.