This article is devoted to solving the problem of manufacturing products from carbon fiber composite materials, which are obtained as a result of layer-by-layer laying of carbon fiber with impregnation of their binder components. This paper presents a description of the process of spiral winding of products on a cylindrical mandrel and the mathematical model, which takes into account the coefficient of friction and the necessary reverse zones in which the tape will not slip. The model is implemented as a Python program and is capable of simulating and visualizing the step-by-step winding of a carbon tape on a cylindrical surface. It is possible to optimize the friction coefficient to ensure the tightest winding of subsequent passes. The program takes into account reverse zones, which are calculated taking into account the friction coefficient of the cylindrical mandrel. Based on the simulated winding process, a control program for the robotic arm is generated. The performance of the proposed model and its implementation was tested on a test bench with a robot.