The invention relates to a screw press apparatus (1) comprising an outer casing (2) surrounding a screening tube (6a) with a plurality of liquid discharge holes, a slurry inlet port (3) at one end of the screening tube and a solids discharge port (4) at an opposite end of the screening tube, the screening tube housing an axially located auger (5), the outer casing (2) having a first opening in fluid communication with the slurry inlet port (3), a second opening in fluid communication with the solids discharge port (4), and a third opening (8) in fluid communication with the liquid discharge holes of the screening tube (6), a cleaning device (20) located between the outer casing and the screening tube, a device (10) for axially moving the cleaning device. The cleaning device (20) has a rigid co-axial liquid supply pipe (30) having at least one washing pipe (21, 22, 23, 24) at least partially surrounding the screening tube (6), each at least one washing pipe (21, 22, 23, 24) containing a plurality of nozzles (211, 221, 231, 241) facing the screening tube (6a). The screw press apparatus is especially suited for processing protein containing slurries, and in another aspect the invention relates to a method of producing a gluten product using the screw press apparatus.