An inflatable mattress for supporting patients comprises two inflatable longitudinal tubes (1, 2) extending along the respective longitudinal edges of the mattress and a plurality of inflatable transverse tubes (3, 3'). Each transverse tube (3 or 3') has adjacent its end an aperture (9a), with the longitudinal tube (1) extending through the aligned apertures (9a) at one side of the mattrress and the longitudinal tube (2) extending through the aligned apertures (9a) at the other side of the mattress. The transverse tubes are selectively inflatable in various modes under microprocessor control.