Introduction. In this study, a model is developed which describes the local filtrate flux and the distribution of local solids concentration in the filter channel during steady-state cross-flow membrane filtration of colloidal suspensions. Unlike the previous models available in the literature (Bacchin et al., 2002), which predicts filtration kinetics for a model system with incompressible deposit layer and Newtonian concentration polarization (CP) layer, the proposed model considers essential factors for filtration, including the complex rheological behavior of the filtered material over a wide concentration range, encompassing both Newtonian and non-Newtonian characteristics. Additionally, the model takes into account the compressibility and permeability of the filtered material. Experimental/methodology. Analytical solution of a system of mass and pressure balance equations under the assumption of a thin CP layer yields the local filtrate flux distribution along the membrane, J(x): (a) where J(0) is the filtrate flux across the membrane in the absence of the concentration polarization, c0 is the solids concentration in the bulk, μf is the filtrate viscosity, x is the distance from the entrance to the filter channel, and M(csg, τw) is the integral characteristics of the filtered material, which is defined as (b) (where τw is the applied wall shear stress, and csg is the sol-gel transition concentration, i.e. the maximal solids concentration in the CP layer). Results and discussion. A multiparameter numerical study of the influence of rheological behavior, compressibility and permeability of the filtered material on filtration kineticswas carried out. Notabely, the importance of accounting non-Newtonian behaviour of CP layer was highlited. According to the model, the filtrate flux remains independent of the properties of the deposit. This implies that there is no necessity to define or measure properties of filterred material (rheological, compression and permeability properties) for concentrations exceeding csg (c > csg). For c > csg, however, these properties could be utilized to predict the local solids concentration in the deposit, c(x,z), using the integral form of Darcy’s equation, where z represents the normal distance to the membrane surface.