The invention relates to a press (1) for separating fat containing mass, e.g. cocoa mass, into liquid fat and cake, comprising a frame (2), a plurality of pressing elements (6) disposed in the frame (2), and a hydraulic cylinder and plunger (3, 3A) for exerting pressure on the pressing elements (6), the pressing elements (6) comprising a pot (7) having a cavity (8) for receiving mass to be pressed, a squeezer (9) located at least partially in the cavity (8), and filters (11) disposed in front of the squeezer (9) and on the side of the cavity (8) opposite the squeezer (9), wherein, in the filling position of the press (1), the distance between the filters (11) is in a range from 10 to 90 mm. The ratio (Dc/Dp) of the diameter (Dc) of the hydraulic cylinder (3) and the diameter (Dp) of the cavities (8) is smaller than 1,15.