The flow of granular materials through curved or straight discharge chutes is classified as either “fast” or “slow.” Fast flow is the more efficient and occurs when the material flows in contact with the chute bottom and side walls, but does not make contact with the top. On the other hand, slow flow occurs when the material is in contact with all four faces of the chute. Under fast flow conditions, the grain stream thickness varies along the chute with the minimum thickness occurring near the point where the mean stream velocity is a maximum. The paper investigates the conditions governing fast flow and presents an approximate analysis to account for the grain stream thickness variation. The analysis, based on the assumption of steady flow, involves the solution of nonlinear differential equations. An equivalent friction coefficient is introduced to account for the frictional drag on the chute bottom and side walls; this friction coefficient is not constant but is found to vary with the changing stream thickness. Results of experimental investigations performed on chutes of known geometric shape are correlated with the analytical solutions. High-speed cine photography is used to determine the actual velocities and paths of individual grains in the moving stream, thus enabling the velocity profiles to be determined at different points along the stream. The paper presents data and recommendations for optimum chute design. These data include suggestions relating to the best chute shape to meet a given set of conditions and information concerning the optimum chute cutoff angles to avoid flow obstructions.