Vibrating screens are a widely applied form of particle separations. In spite of this significance, their understanding is still an obstacle. Three approaches were used to characterize the flow of granular material in a linear vibrating screen. The statistical model, mass action, and kinetic model based on conservation of momentum were derived. Experiments were then conducted on a multi-sized prototype screen and glass beads of sizes 0.75, 1, 2, 3 mm. Deck inclinations were varied over 7.5,12.5, and 17.5 degrees, and frequencies over 7, 15, and 20 Hz. A total of 72 feed batches and a constant power of 50 W was used. The experimental data was then used to validate the models. The three models provided accurate flow prediction over the screens. Additionally, the kinetic model also provided a basis for optimal design of the screening unit operation, by allowing manipulation of seven design variables to obtain a 95-100% efficient vibrating screen. (c) 2016 American Institute of Chemical Engineers AIChE J, 62: 3889-3898, 2016