Deep bed filtration of water with particles occurs in several industrial and environmental processes like water filtration and soil contamination. In petroleum industry, deep bed filtration occurs near to injection wells during water injection, causing injectivity reduction. It also takes place during well drilling, sand production control, produced water disposal in aquifers, etc. The particle capture in porous media can be caused by different physical mechanisms (size exclusion, electrical forces, bridging, gravity (sedimentation), etc.). In case of size exclusion mechanism, the larger are the particles and the smaller are the pores, the more intensive is the capture and the larger is the formation damage. Nevertheless, the widely used traditional model does not account for particle and pore size distributions. Considering that particles are captured due to size exclusion mechanism, we derived basic equations for transport of particulate suspensions in porous media, accounting for particle and pore radii distributions. Particles are carried by water flowing through the accessible pore space only, i.e. particles cannot access smaller pores. In the current work, the effects of porous space accessibility and particle flux reduction due to selective flow of different size particles are included into the stochastic deep bed filtration model. The particle and pore ensembles for analytical solutions of the derived system show more realistic physics behaviour than that of the traditional model. Averaging of the derived stochastic equations leads to a new deep bed filtration model that significantly differs from the classical deep bed filtration system. Treatment of several experimental data shows good agreement between the laboratory and modelling data and validates the proposed model. The derived stochastic model has been extended to model formation of external filter cake by particles from the injected polydispersed suspension, allowing treating both deep bed filtration and external filter cake formation in the framework of the same system of governing equations.