The article presents the results of theoretical studies to determine the patterns of movement of cotton fly on a flat surface of the grid. A structural scheme and the principle of operation of the multifaceted mesh surface of a cleaner of fibrous material from fine waste is given. Analytical methods have obtained expressions for determining the movement of fibrous material on a mesh surface. By numerically solving the problem of the impact interaction of a fibrous material with a multifaceted grid, graphical dependences of the parameters of the fiber treatment zone are constructed.