A tracheostomy tube assembly has a tube (1) and a flange assembly (2) that can be moved along the machine end region (10) of the tube. The flange assembly has a screw clamp (36) that can be tightened to apply a compressive force to the outside of the tube to lock the flange assembly in position. The machine end region of the tube has a non-circular section that is wider along the axis (15) along which the screw clamp applies a force. In this way, when the screw clamp (36) is tightened to lock the flange assembly (2) in position the tube (1) in the region of the clamp is deformed to a more circular shape. This avoids gripping any inner cannula (20) within the tube (1).