A uni-directional rigidifier for a foldable mattress for use in sofa beds has an arcuate, elongated shape. Lateral slits along the rigidifier allow it to easily flex when a load is applied while in an upright position. When the rigidifier is in an inverted position, an applied load causes the slits to close and the rigidifier to stiffen. The method describes the use of the uni-directional rigidifier in a foldable sofa bed mattress.