Abstract: An inflatable mattress is of an elongated plan form and comprises a plurality of inflatable cells also of an elongated form which are disposed contiguously in a row extending along the longitudinal axis of the mattress. Constraints of a tray-like form circle the cells so as to retain them in a position with their upper ends exposed whereby by the upper ends form a resilient support surface. The cells are formed with pleats so that when a body is placed on the resilient upper surface the support surface material is not tensioned substantially. A cell is of a flexible sheet material and comprises an inner sheet disposed between outer sheets. The outer sheets are secured by spot welds to the inner sheets. Inflation air can flow freely between opposite sides of the inner sheets. The spot welds on each side of a cell define a series of sub-cells. The mattress may be "tuned" so as to change the yield characteristics of a cell.