A therapeutic, self-inflating mattress (1) of reticulated, open-cell foam comprises an airtight and watertight surface coating (5a, 5b) and equipped with at least one valve (4a, 4b). The mattress (1) comprises two superimposed layers (2, 3) of reticulated open-cell foam with an adhesive layer (6) between them, a bottom layer (3) of high resilience (HR) foam and a top layer (2) of visco-elastic foam, the two-layer assembly being covered with at least one film or coating of a polymer binder covering the entire outer surface of said two-layer assembly except in the vicinity of the at least one valve.