A support device capable of supporting a patient, including a mattress (10) resting or capable of resting on abed base or bed frame (11) including, either a1) means for adjustment of the length of the mattress by means of pneumatically independent inflatable transverse cells (8-1, 8-4), forming a retractable area (8), and a2) means for grouped movement of an end area (9) adjacent to said retractable area, and/or b) means for adjustment of the width of the mattress, including at least one lateral inflatable cell (2, 2a, 2b), extending in the longitudinal direction (XX) of the mattress.