An epidural catheter has a closed, soft patient end region with a side opening. The catheter is formed from a two-layer extruded tube in which the outer layer is of a harder material than the inner layer. A heated pin is inserted in one end of the tube to expand its diameter. An annular grinding tool is then moved along the expanded region to remove the outer, hard layer in this region. The end of the tube is subsequently closed and the side opening is formed.