A one-dimensional modelling of constant pressure deliquoring based on not more than three material specific parameters was achieved by the following basic assumptions : two regions of void ratio are defined. From the initial value down to a threshold value e(i), the solid-solid interaction is neglected; only when the water content falls short of e(i), an elastic network with increasing elasticity modulus is formed. Filtration and consolidation are not regarded as subsequent stages, but are assumed to occur at varying extents during the whole process. The profile of porosity is approximated by a rectangular function while the profiles of liquid pressure and the elasticity modulus inside the compressed zone are approximated by hyperbolic functions. The compressed zone is characterized by an average solid stress sigma(c) and an average filtration resistance R(c) both related to the volume of the expressed or filtrated liquid V (maximal amount V(E)). The proportionality between sigma(c) and V and that between dR(c) and dV/(V(E) - V) are inherent empirical conditions. For the initial stage of solid-liquid separation, a strong non-linear profile of the filtration resistance results and this is discussed usually to be due to a "skin effect". The model was successfully applied to the kinetics of the press-dewatering of different materials : suspension of protein, sawdust, semi-solid clay and sugar-beet tissue. Additional parameters describing the secondary consolidation were not required. Filtration was shown to be a boundary case of the model.