A screw press has a cylindrical screening section mounted to a frame. The screening section is able to rotate but can be prevented from rotating. A sprayer system is operable to spray water on the screening section. In a cleaning process, the screening section is rotated while water is sprayed against it. Optionally, the power required to rotate the screen may be provided by an auger drive mechanism. The screening section may have openings sized to retain flocculated solids. The screw press may be used to thicken a sludge from a waste water treatment plant.