A dual lumen cannula for use in haemodialysis has an improved leading end to facilitate insertion and an improved coupling for connection to blood extraction and return tubes. The improved leading end has a conical tip centered on the longitudinal axis of the cannula and, in the leading end, the extraction lumen is blanked off by using an insert to prevent blood flow downstream of the extraction lumen, and to minimize blood stagnation and damage. The improved coupling is generally Y-shaped and the extraction and return lumens of the cannula terminate in conical shaped ends which receive extraction and return tubes with similar shaped ends. The ends of the extraction and return tubes have minimal thickness so that when inserted the interior surfaces of the cannula lumens and the tubes merge smoothly to minimize blood impact problems. Methods of manufacturing the tip and a Y-shaped connecting piece for connecting the dual lumen cannula to tubing are also described.