A guide wire for guiding a medical device within a patient is disclosed. The guide wire has a solid inner core made of high modulus material such as Conichrome® or a rhenium alloy, and an outer shell made of a flexible, kink resistant material such as a nickel-titanium alloy. Preferably, the modulus of elasticity of the inner core material is at least about 20 percent greater than that of the outer shell material. The outer shell is mechanically joined to the inner core through a drawing or cladding process. In various embodiments, the distal end of the guide wire can be tapered by grinding away the outer shell to expose the inner core. Because of its stiffness, it can be manually shaped by the physician or cardiologist.