The constitutive equations proposed by Tiller and Shirato were analyzed and a new constitutive equation originating from the sediment thickness was proposed. A new boundary condition of the filter cake based on the solid compressive pressure of the first solid layer, pf, was also proposed. Accurate average specific cake resistances at various pressures and the thickness of cake were calculated with the new constitutive equation and boundary conditions. The influence of pf on the cake thickness and average porosity was studied theoretically. Using three constitutive equations, it was proved that the compressibility n obtained from filtration results instead of CPC (compression-permeability cell) of very compressible cake could not have an exact value.