Steerable catheter that has fluid transfer capability is provided. The catheter includes an elongate flexible shaft having a proximal end and a distal end, an operative element carried at the distal end of the shaft, and a medium conveying conduit carried within the elongate shaft, the conduit having a distal end that is affixed relative to the distal end of the elongate shaft, and a proximal end that is configured to move relative to the proximal end of the shaft. In this manner, the proximal end of the medium conveying conduit is allowed to slide relative to the proximal end of the shaft as the distal end of the shaft changes shape, thereby preventing kinking of the conduit.