A steerable catheter sheath for use in directing a catheter into a desired position is provided. The sheath includes an elongated member configured to receive the catheter therein. The distal end of the elongated member is steerable in two directions, each direction having a different bent configuration, e.g., a sharp curve in one direction and an open arching curve in the other direction. A resilient structure having different bending properties in each of its lateral sides is carried in the distal portion of the elongated member and causes the asymmetric bending. In one embodiment, the resilient structure includes a hypotube with a plurality of notches and slits in the sides. In another embodiment, the resilient structure is covered in an outer coating having different durometer portions. The sheath is particularly useful for accessing left and right pulmonary veins when a transeptal entry approach is used into the left atrium.