Local hand vibrations can cause occupational diseases in drivers of heavy motor vehicles, such as white finger syndrome. In this study, a method has been developed to check the diameter of the steering shaft from the aspect of hand fatigue due to the action of tangential vibrations of the steering wheel, as tangential accelerations occur in it due to torsional vibrations, as an elastic system. By applying the method of “stochastic parametric optimization”, the diameter of the steering shaft was calculated from the aspect of minimizing tangential accelerations. Based on this value, the tangential vibrations of the steering wheel were calculated and compared with the ISO 5349/DIS criteria. Since the obtained values of analyzed accelerations are lower than the mentioned criteria, the calculated diameter of the steering shaft can be used for further analysis. More precisely, it should be compared with the one on the derived steering mechanism and, as authoritative, adopt the larger one.