Improving the efficiency of the process of separating fiber from cotton seeds by improving the working chamber of the gin is one of the important issues. The main way to increase the efficiency of sawn gin is to increase the fiber content in the mass of seeds in the working chamber with a uniform decrease in its density. This can be achieved by using grates with a concave working surface, which serves to move the seeds away from the rotating saws and accelerate the release of bare seeds from the working chamber. The article discusses the movement of seeds on the concave surface of the grate and determines the rational parameters of their working part. The article explores the proposed grate model, consisting of four geometric shapes, provides an analytical analysis of the geometric types. The dependence of the location of the last rectilinear part of the general contour on the shape of its convexity and concavity is determined. Cotton seeds move along the contour in the form of a stream. We assume that the thickness of the flow along the contour is constant and equal. We compose a unique equation of the flow in each section of the circuit. To determine the state of the flow, we denote its velocity, density and pressure in each section, respectively. Let us determine the flow motion along the contour with respect to the arc.