An inflatable component (4) for an alternating pressure mattress (1). The inflatablecomponent has at least two inflatable cells (15). Each cell (15) has at least twoopposite edges (23, 24) and at least part of one of two opposite edges is free andlies within an outer peripheral edge of the component. The inflatable component(4) may be formed from two layers of material joined together along predeterminedlines to define the cells. The inflatable component may include two or more groupsof cells, each connected to a respective air inlet (19, 20). The inflatable componentmay be comprised in a mattress.