Using　classical　constant-pressure　molecular　dynamics　simulations　and　the　force　constants　model,　radial　breathing　mode　(RBM)　transition　of　single-wall　carbon　nanotubes　under　hydrostatic　pressure　is　reported.　With　the　pressure　increased,　the　RBM　shifts　linearly　toward　higher　frequency,　and　the　RBM　transition　occurs　at　the　same　critical　pressure　as　the　structural　transition.　The　group　theory　indicates　that　the　RBMs　are　all　Raman-active;　however,　due　to　the　effect　of　the　frequency　transition　and　the　electronic　structure　change　for　tube　radial　deformation,　the　Raman　intensity　of　the　modes　becomes　so　weak　as　not　to　be　experimentally　detected,　which　is　in　agreement　with　a　recent　experiment　by　S.　Lebedkin　[Phys.　Rev.　B　73,　094109　(2006)].　Furthermore,　the　calculated　RBM　transition　pressure　is　well　fitted　to　the　cube　of　diameter　(similar　to　1/d(3)).