Abstract: A steerable dilatation catheter which is particularly adapted for angioplasty procedures having a concentric construction of thin-walled inner and outer tubular members of high strength plastic, such as polyimide, which provide diametric rigidity but longitudinal flexibility. At least the distal portion of the inner and outer tubular members which will extend out of the guiding catheter during angioplasty procedures have wall thicknesses of less than 0.002 inch, preferably less than 0.0015 inch. An elongated core member is adapted to freely rotate within the inner tubular member but is prevented from any significant axial movement therein.