Mattress (1) for beds (2) adapted to incorporate the body of a person (P) stretched when passing from a rest position to an operative position, of the type of beds (2) that have a frame (3), tilting around at least one transverse axis (4a), on which a mattress (1) rests, at least one first head-back support area (1A) being determined on the mattress (1) followed by a second area buttocks (1B), capable of being arranged forming a plurality of angles between 180º and 90º to each other when tilting the frame (3), and the mattress (1) comprising a first lower semi-mattress (5) made of a first material and a second upper semi-mattress (6) made of a second material, of less thickness than that of the first lower semi-mattress (5) and which is provided with a support surface (7) intended to support a person (P), being the mattress (1) characterized in that - the first lower half mattress (5) and the second upper half mattress (6) are arranged superimposed on each other and face one of their two faces (51.61) with a greater surface area, the second upper half mattress (6) being located above the first lower half mattress (5) in the rest position and in the operating position: - the first head-back support area (1A) of the mattress (1) is formed by a first head-back support part (5A) of the first lower half-mattress (5) and by a first head support part- back (6A) of the second upper half mattress (6), arranged facing each other on respective opposite faces (51A, 61A), and the second glute seating area (1B) of the mattress (1) is formed by a second seat part of buttocks (5B) of the first lower semi-mattress (5) and by a second butt-seating part (6B) of the second upper half-mattress (6) arranged facing each other on respective opposite faces (51B, 61B), - the first lower half mattress (5) and the second upper half mattress (6) are connected to each other by at least their respective second buttock seating parts (5B, 6B)； and because - the corresponding opposite faces (51A, 61
