The apparatus comprises a carousel (1), rotatable about a central axis (2) with respect to a base frame (3). To the carousel (1) many couples of forms (4 and 4') are connected, cantilever mounted, which follow a circular trajectory indicated as dotted line. The couples of forms (4 and 4') can be arranged, radially or parallel to each other, on the carousel substantially according to the sides of a polygon. The forms have anatomical shape like a leg with foot end and are stiff enough from staying vertical oriented towards the above. The carousel moves through a loading station (5) of the stockings on the forms (4,4'), a station (6) for stretching the stockings on the forms; a steaming station (7), for steaming the stockings; an air drying station (8) and an outlet station (9) of the finished articles. At each station of the carousel the tights present on the couples of forms (4 and 4') are treated at the same time or in turn. The carousel (1) comprises a tubular body (10) having a prismatic wall (11), pivotally connected to the base frame (3). The wall (11) has the main function of rotating, and then to be the frame of the carousel (1), and it holds also radially the forms (4) arranged as cantilevers so that they do not extend from the bases. A steaming chamber (20,20') is provided that can move from an open position that allows the free rotation of the forms (4,4') to a closed position that embraces completely both couples of forms (4,4') sealingly contacts the wall (11).