[Problem to be solved] The present invention provides a medical Ti-Ni alloy largely including a TiNi single phase, in which both strength and plasticity of the metal material at the body temperature are maintained, and formation of a knife-edged fracture surface when bending and breaking is less significant. The medical Ti-Ni alloy can be used for cores of catheters, guide wires and the like.[Solution] The present inventors find that above objective can be achieved by using an alloy largely including a TiNi single phase. Then the present invention has been completed.