Using the optimal control theory, the problem of finding profiles of gravity flow discharge chutes required to achieve maximum exit velocity of granular material under the speed dependent resisting forces is solved. A model of a particle moving down a curve which is treated as a unilateral constraint is used. The fast flow condition and the condition that the particle does not leave the curve are introduced as the additional inequality constraints. The influence of the initial particle speed and the power of the speed in the expression for the resisting force on the optimal chute profile are analyzed. (C) 2014 Elsevier B.V. All rights reserved.