An inflatable cell that is inflatable with a fluid, such as air, comprises a flexible casing that is closed at its ends, the casing defining, between its walls, at least one inflatable chamber; and at least one fluid insertion means for inserting fluid into the chamber and at least one fluid removal means for removing fluid from said chamber, these insertion and removal means being bonded in substantially airtight manner to at least one end of the casing; and at least one link means for linking the cell to another identical cell, which link means are integral with or secured to the casing. A method of manufacturing such a cell and a support device of the mattress type that is manufactured on the basis of assembling together such cells are also disclosed.