A drainage catheter is adapted to drain fluid from the body cavity through a body conduit and includes an elongate tube and a retention member disposed at the distal end of the elongate tube. The retention member is adapted for movement between a low-profile state facilitating insertion of the catheter and a high-profile state facilitating retention of the catheter in its operative position. A woven mesh forms at least a portion of one of the tube and the retention member. The woven mesh can be formed of filaments heat-settable so that the catheter automatically moves to the high-profile state. Insertion of the catheter can be facilitated using a stylet which can be removed after insertion to permit the catheter to automatically return to its high-profile state.