This article is devoted to the development of a mathematical model of the important method producing goods from composite materials – winding of continuous fibers in the force direction. The paper considers a problem to find the optimal trajectory and a law of motion of the spreading mechanism of a numerical control winding machine for making complex-shaped constructions of fibrous composite. The problem is solved taking into account a real structure of tape of fibrous composite, restrictions on an allowable position of the spreading mechanism, a thread tension and a broaching speed of tape.