Up to now, the non-linear partial differential equation of filtration has not been solved, and the variation of hydraulic-pressure, flow rate of liquid and porosity in cake can only be analyzed by means of numerical techniques and compression permeability simulation in this paper, an analytical solution of the filtration differential equation, is obtained in the form of error functions. The distribution of hydraulic pressure P(L) in the cake is discussed. It is shown that P(L) distribution is affected not only by cake compressibility, but also by operational conditions such as slurry concentration and filtration pressure. In addition, two deliquoring mechanisms are presented-surface filtration and solid cake compression. A parameter beta is proposed to stand for the relative contribution of the surface filtration and solid compression to solid-liquid separation.