The　integration　of　ferroic　oxide　thin　films　into　advanced　flexible　electronics　will　bring　multifunctionality　beyond　organic　and　metallic　materials.　However,　it　is　challenging　to　achieve　high　flexibility　in　single-crystalline　ferroic　oxides　that　is　considerable　to　organic　or　metallic　materials.　Here,　we　demonstrate　the　superior　flexibility　of　freestanding　single-crystalline　BiFeO3　membranes,　which　are　typical　multiferroic　materials　with　multifunctionality.　They　can　endure　cyclic　180　degrees　folding　and　have　good　recoverability,　with　the　maximum　bending　strain　up　to　5.42%　during　in　situ　bending　under　scanning　electron　microscopy,　far　beyond　their　bulk　counterparts.　Such　superior　elasticity　mainly　originates　from　reversible　rhombohedral-tetragonal　phase　transition,　as　revealed　by　phase-field　simulations.　This　study　suggests　a　general　fundamental　mechanism　for　a　variety　of　ferroic　oxides　to　achieve　high　flexibility　and　to　work　as　smart　materials　in　flexible　electronics.