A catheter for hemodialysis comprises a flexible catheter tube defining a plurality of separate lumens. The catheter defines an arc angle of generally U-shape in its natural, unstressed configuration. Thus, the catheter may be implanted with a distal catheter portion residing in a vein of the patient, the distal catheter portion being of substantially the shape of the vein in its natural, unstressed condition. Also, a proximal catheter portion resides in a surgically created tunnel extending from the vein and through the skin of the patient, this section of the catheter also being typically in its natural, unstressed condition. Thus blood may be removed from the vein through one lumen of the catheter, and blood may be returned to the vein through another lumen of the catheter, while the catheter is subject to long term indwelling in the body. Improved results are achieved because of the lack of mechanical stress in the shape of the catheter, which stress causes the catheter to press unduly against adjacent tissues.