An inflatable and deflatable balloon catheter is disclosed. The inflatable chamber of the catheter is supported about an elongated support member of small diameter. One end of the support member is rotatable relative to the chamber wherein the chamber is adapted to being compactly twisted about the support member upon swiveling or rotation of the support member. The compactly twisted chamber has a small diameter whereby insertion of the catheter through a small incision and guiding thereof in a small body canal or passage is facilitated. A smooth-walled sheath of low friction material is disclosed for enclosing the twisted chamber to facilitate atraumatic entry of the catheter into the incision or body opening and for facilitating insertion and movement of the catheter. The support member is preferably made of a material which may be formed during use into a desired axial configuration by bending. Balloon catheters according to the present invention are advantageously used for intra-aortic balloon pumping.