A wound dressing includes a tube (9) for evacuating fluid from a wound and an air-tight and liquid-tight envelope layer (10) of flexible material, which envelope layer has a central region, in which the tube emerges beneath the envelope layer, and a peripheral region, which extends beyond the central region, the tube from the central region running outwards into the peripheral region beneath the envelope layer and out from this. The tube (9) is enclosed in a pressure-distributing material piece (11) which surrounds the tube, extends along the tube in the peripheral region, and also extends laterally beyond the tube viewed in the longitudinal direction of the tube.