An improved vascular catheter for angioplasty providing a variable stiffness lengthwise of the catheter. A relatively stiff shaft portion is provided for transmitting the necessary axial forces for advancing the catheter along a guide wire through a series of sharp bend to the arterial branch for dilatation, and a more flexible waist portion connects from the shaft to the balloon and tip portion. This allows the tip and balloon portions to follow sharply bending turns in the guide wire without the shaft portion tending to push the tip beyond a branch or dislodge the guide wire. A set of such catheters may be provided for a surgical procedure, having varying lengths of the waist portion according to the circumstances of the case. If a sharp turn is encountered that cannot be tracked, the catheter can be withdrawn leaving the guide wire in place, and another catheter of the set having a longer waist portion can be inserted to successfully follow the turn.