To obtain a fundamental understanding of the various factors affecting pressure filtration performance, we developed a coupled computational fluid dynamics (CFD) and discrete element method (DEM) model for simulating the effect of solvent flow through the solid particle cake. The model was validated using data collected by filtering mixtures of spherical glass beads and deionized water through a dead-end cell over a range of applied pressures. Numerical experiments were performed to study the effects of particle properties, liquid properties and operating conditions on filtration performance. The model predicted that the filtrate flow rate could be strongly affected by the mean size of the particles, the presence of small particles (i.e. fines) in the particle distribution, the viscosity of the liquid, and particle deformation leading to cake compression. Our study demonstrated that CFD-DEM modeling is a powerful approach for understanding cake filtration processes and predicting filtration performance.