A model is presented for the dewatering of a saturated two-phase medium in a screw press. The model accounts for the detailed two-phase rheological behaviour of the pressed material and splits the press into two zones, an initial well-mixed constant-pressure region followed by an axial transport region in which the total pressure steadily increases. In this latter region, a slowly varying helical coordinate transformation is introduced to help reduce the dynamics to an annular bi-axial compression of the two-phase medium. Unlike previous modelling, the transition point between the two zones is determined self-consistently, rather than set a priori, and the pressure along the length of the press is deduced from the rheology of the two-phase ...