A model describing hydrodynamics of a filtering slurry system is presented, incorporating axial effects in the entire slurry volume as well as radial effects at the axial positions where a filter is present. It is demonstrated that the model is capable of handling all different types of hydrodynamic steady states that may occur. Model predictions with respect to build-up of filter cake are compared to previously reported results of experiments and calculations using a model neglecting axial variations at the positions where a filter is present. In the experimental range of interest quantitative results (especially for the surface renewal model) are slightly altered when taking axial variations in the filter zone into account. However, after fitting the unknown model constants to experiments, the relevant trends remain unchanged as compared to previous results. The physical meaning of dimensionless numbers derived from the model equations is discussed as well as the implications different values for these numbers (not limited to the experimental range) have on model results. It is also demonstrated that when applying the force balance model to describe radial hydrodynamics, a relatively uniform cake distribution is observed as compared to applying the surface renewal model. A physical explanation is offered for the existence of a maximum allowable filter length as mentioned in literature for systems free of filter cake. Implications of model results for design of filtering slurry systems are given.