Abstract: An air-support mattress comprises an elastomeric plate having upper and lower faces flanking a central neutral surface. This plate is formed with a network of passages which lie between the lower face and the neutral plane and are adapted to be connected to a source of fluid under pressure. The plate is further formed with an array of vents each extending from the passage across the surface and terminating at respective mouths at the upper surface. A pair of lips in each of the vents meet tangentially between the neutral surface and the passage so as normally to block air flow through the vents. When the upper surface of the mattress is rendered concave, however, these lips pull apart so as to allow a stream of air to flow from the vents and exert a supporting force on a body part depressing the mattress.