This paper presents a numerical study of particle flow and sieving behavior on a vibrating screen. The particle flow is modeled by means of discrete element method (DEM) at a particle scale. The DEM model is first verified by the good agreement between the numerical and experimental results in terms of the distribution of percentage passing of different sized particles along the screen deck. The effects of variables such as incline angle, vibrating frequency, and amplitude are then studied with special reference to the overall screen efficiency and distribution of the passing rates for different sized particles. The performance of such a screening process is shown to be related to particle flow on the screen such as the structure of particle bed, particle velocities, and particle-particle and particle-deck interactions. In particular, it is demonstrated that the sieving performance at the process equipment scale can be linked with the particle-deck collisions obtained from the DEM simulations, facilitated by the well-established probability theory. Finally, based on the simulation data, a mathematical model is proposed to link the particle-deck collisions with the three variables considered. The mathematical model can satisfactorily estimate the process performance in terms of weight percentage passings, particularly when the effect of particle-particle interactions is not significant.