A method for the treatment of thrombosed hemodialysis access grafts or fistulas defining a shunt positioned between an arterial side and a venous side is achieved by inserting a balloon catheter within the shunt, wherein the balloon catheter includes a distal balloon and at least one infusion aperture located proximally of the distal balloon. Thereafter, the balloon catheter is advanced within an arterial anastomosis at an artery-shunt juncture and the distal balloon is inflated. A thrombolytic agent is then injected through the infusion apertures of the balloon catheter into the shunt to chemically destroy clot material within the shunt, wherein by applying the thrombolytic agent with the distal balloon inflated at the arterial anastomosis the possibility of the clot material moving into the artery is prevented and there is no need to worry about the migration of the clot into the arterial system and the resulting complications. Finally, the inflated distal balloon is pulled toward the venous side, eradicating the arterial plug. A balloon catheter for use in accordance with the present invention is also disclosed.