Models for rotary drum and disc filtration of compressible suspensions are developed using one-dimensional compressional rheology theory. The models account for cake formation while the drum or disc is submerged in the feed slurry, saturated cake consolidation upon surfacing due to capillary pressure, and cake desaturation. Desaturation does not occur for vacuum pressures below a critical value given by the material properties, or is incomplete if the formation and consolidation angles are too large. The disc filter model is formulated by applying the drum filter solutions to concentric annuli. The effect of different operating parameters such as submerged depth, rotational rate, slurry concentration, and vacuum pressure are investigated. The throughput varies linearly or quadratically with the drum or disc radius respectively, proportionally with the square-root of the angular rotational speed and linearly with the submerged angle. The angles for cake consolidation and desaturation are independent of the rotational rate. (C) 2010 American Institute of Chemical Engineers AIChE J, 57: 951-961, 2011