We　study　the　Rayleigh-Taylor　instability　problem　for　two　incompressible,　immiscible,　viscous　magnetohydrodynamic　(MHD)　flows　with　zero　resistivity　and　surface　tension　(or　without　surface　tension),　evolving　with　a　free　interface　under　presence　of　a　uniform　gravitational　field.　First,　we　reformulate　the　MHD　free　boundary　problem　in　an　infinite　slab　as　a　Navier-Stokes　system　in　Lagrangian　coordinates　with　a　force　term　induced　by　the　fluid　flow　map.　Then,　we　analyze　the　linearized　problem　around　the　steady　state　which　describes　a　denser　immiscible　fluid　lying　above　a　light　one　with　a　free　interface　separating　the　two　fluids,　and　both　fluids　being　in　(unstable)　equilibrium.　By　studying　a　family　of　modified　variational　problems,　we　construct　smooth　(when　restricted　to　each　fluid　domain)　solutions　to　the　linearized　problem　that　grow　exponentially　fast　in　time　in　Sobolev　spaces,　thus　leading　to　an　global　instability　result　for　the　linearized　problem.　Finally,　using　these　pathological　solutions,　we　prove　the　global　instability　for　the　corresponding　nonlinear　problem　in　an　appropriate　sense.　Moreover,　we　evaluate　that　the　so-called　critical　number　indeed　is　equal　to,　and　analyze　the　effect　of　viscosity　and　surface　tension　on　the　instability.　©　2014　Copyright　Taylor　and　Francis　Group,　LLC.