An epidural catheter 1 with a soft tip 2 is made by co-extruding an inner layer 11 and
an outer layer 12, the inner layer being of a stiffer plastics that the outer layer. The extrusion
machine 20 has two extrusion heads 21 and 22, the one 21 for the inner layer 11 having a
movable cone 29 that is moved in periodically to increase the internal diameter of inner layer
and then to cut off flow of extrudate entirely. This produces a region 13 having a part 14 with
a thinner inner layer 11 and part 15 where the inner layer is absent. The tubing 40 is cut at the
end of these regions 13 which are then closed and formed with a side opening 3 so that the
patient end tip 2 is less stiff than the remainder of the catheter.