The vehicle steering system is one of the most important systems on the vehicle, both in terms of safety and performance. Based on the geometry of the steering trapezoid, the geometry of the suspension system, the alignment angles of the wheels, as well as the characteristics of the tires, a mathematical model for the design of the formula student vehicle "Road Arrow" steering system was developed. Based on the dynamic state of the vehicle, the mathematical model provides information on the stress of the steering system, the torque on the steering wheel and the slip angles of the steered wheels. The mathematical model was developed using the MATLAB software, and validation of the results was performed by comparing the results with the ones obtained by simulations in MSC ADAMS. Analysing the obtained results, it is possible to conclude that the average value of relative error of the stress is approximately 15%, for slip angles of the steered wheels is approximately 7%, and the error for torque on the steering wheel is approximately 6%.