The present invention provides a catheter for the delivery of fluid medication across an anatomical region. In accordance with one embodiment, the catheter comprises an elongated tube with a plurality of exit holes along an infusion section of the catheter, and an elongated flexible porous member residing within the tube and forming an annular space between the tube and the member. In accordance with other embodiments, the catheter includes a tube having a plurality of exit holes in a side wall of the tube. The exit holes may combine to form a flow-restricting orifice of the catheter. In one particular embodiment, the catheter comprises a tube having elongated exit slots therein. In accordance with other embodiments, the catheter includes an elongated tubular member made of a porous membrane. In accordance with other embodiments, the catheter includes an elongated "weeping" tubular coil spring attached to an end of, or enclosed within, a tube.