A tunnel dressing for use in treating a tunneling wound using negative pressure wound therapy. The tunnel dressing includes an elongate permeable member having a closed distal end for entering the wound and an open proximal end into which an applicator is removably disposed for guiding the dressing into the wound. The tunnel dressing has a support structure adapted to transport wound exudates away from the wound and to resist compression under suction. The tunnel dressing also has a wound contact surface adapted to minimize tissue entanglement to facilitate removal. The support structure and wound contact surface may be formed from the same material or from two adjacent layers of different material.