This paper presents a mathematical investigation of particulate motion on an inclined screening chute using the Discrete Element Method (DEM). Special attention has been paid to the implementation of an apertured boundary and the algorithm for allowing particles to pass through apertures or to rebound when approaching the screen surface. Computational experiments have been conducted to examine the undersize particle motion across the material layer and through the apertures for bimodal mixtures comprising two different sizes of spherical polyethylene pellets. Discrete particle motion at different regions along the screen has been discussed in relation to the physical mechanisms inherent in the solids separation process and their determinative role on screening efficiency. Simulations have demonstrated the negative effect of near-mesh size particles and the positive role of relatively large particles on screening operations and the crucial effect of particle segregation in material layers. Comparison of screening rate along the screen with experiments has demonstrated adequate agreement. This computational study has shown the advantages of using DEM to understand the complex solids separation process. Further works are envisaged to focus on the development of advanced experimental techniques and the implementation of DEM for sieving processes involving moving screens