An arrangement for pressing materials containing liquid has mobile press container with an container interior that is divided by a press membrane into a pressure medium chamber and a pressing medium chamber. A filling and emptying opening, which can be closed in a pressure-tight manner, allows material to be pressed to be added to the pressing medium chamber. At least one drainage element is arranged in the pressing medium chamber. An interior of the drainage element communicates with a juice discharge of the press container. A turning device, in which the mobile press container is temporarily received can be rotated during a pressing operation from a filling position, about an angle of less than 360°, more particularly of less than 270°, in mutually opposing directions of rotation about an axis of rotation. There is also described a method for pressing liquid-containing materials.