Understanding deep bed filtration (DBF) is essential for technologies like wastewater treatment, waterflooding in oil reservoirs and membrane filtration. Due to its scientific and industrial importance, DBF has been widely studied and various retention mechanisms (adsorption, bridging, deposition, straining, etc.) have been identified. If straining is operative, pore and particle size distributions play an important role on DBF process. Based on the KT finite volume method, numerical solutions for a population balance model are proposed in this paper. General analytical solutions for this model, which consists of particle population balance as well as straining and pore blocking kinetics, are not available in the literature. Good agreement between analytical and numerical solutions allowed to validate and verify the efficiency of the proposed numerical scheme. The numerical solutions correctly predicted shocks in the suspended particle concentration profiles, presenting good accuracy and small numerical diffusion. The simulations showed that particle transport and retention are strongly influenced by pore blocking. In addition, the larger the particle size, the larger its front velocity and the more intensive is straining.