This paper is concerned with the Cell Model method of addressing hydrodynamic flow through system of solid particles. The starting point of the analysis is the general problem formulation intended for describing a pressure driven flow through a diaphragm which can be considered as a set of representative cells having arbitrary shape and containing any number of particles. Using the general problem formulation, the hydrodynamic field inside an individual representative cell is interrelated with the applied pressure difference and the external flow velocity. To this end, four relationships containing integrals over the outer boundary of a representative cell are derived in the paper. Assuming that the representative cell is a sphere containing a single particle in the centre, the derived general relationships are transformed into outer cell boundary conditions employed in the literature by different authors. The general number of the obtained outer boundary conditions is more than the required number. Accordingly, by choosing different sets of the outer boundary conditions, different models are considered and compared with each other and with the results obtained by others for regular particle arrays. The common and different features of the hydrodynamic and electrodynamic versions of the Cell Model approaches are analyzed. Finally, it is discussed which version of the cell model gives the best approximation while describing pressure and electrically driven flows through a diaphragm and sedimentation of particles.