Based upon a new conception that the solid compressive pressure on a cake surface is not null, almost of all solid-liquid separation operations have been re-examined. For cake filtration, the phenomenon caused by the solid compressive pressure on a cake surface is discussed for thin cake. New expression and hindered sedimentation theories are developed by above new conception using Darcy’s equation. Application of the new conception to centrifugal filtration and tangential filtration is also discussed. Above results lead to the conclusion that cake filtration, expression, hindered sedimentation, centrifugal filtration and tangential filtration can be described with a unified theory, and the main difference between the operations is only the boundary condition of cake.