A medical dressing (10) has a flexible panel (12) with adhesive on one side (16)for attaching to the skin of the patient about a wound. A one-way valve assembly(14) is mounted over an opening in the panel and includes a valve body (26) definingtwo separate fluid passages (66, 68). A valve member (64) is configured to permitair and or/other fluids to flow through a first of the passages (66) in an outwarddirection only so that air and/or other fluids are able to exit the wound throughthe first passage but are prevented from entering the wound through the firstpassage. A removable closure member (70) is provided for selectively closingthe second passage (68) to prevent fluid flow through the second passage. Theclosure member (70) can be removed to enable direct access to the wound throughthe second passage (68). The dressing is particularly suitable for use in occludingan open chest wound.