Hydraulic steering systems for mechanical devices, for example, manipulators or vehicle steering systems, should be able to achieve high positioning precision with high energy efficiency. However, this condition is very often not met in practical applications. This is usually due to the stiffness of the hydraulic system being too low. As a result, additional corrections are required to achieve the required positioning precision. Unfortunately, this means additional energy losses in the hydraulic control system. In this study, this problem is presented using the example of a hydraulic steering system for an articulated frame steer vehicle. This hydraulic steering system should provide the required directional stability for road traffic safety reasons. So far, this issue, connected mainly with the harmful phenomenon of so-called vehicle snaking behaviour, has not been solved sufficiently practically. To meet the needs of industrial practice, taking into account the current global state of knowledge and technology, Wrocław University of Science and Technology is performing comprehensive experimental and computational studies on the snaking behaviour of an articulated frame steer wheeled commercial vehicle. The results of these tests and analyses showed that the main cause of problems that lead to the snaking behaviour of this vehicle class is the effective torsional stiffness of the hydraulic steering system. For this reason, a novel mathematical model of the effective torsional stiffness was developed and validated. This model comprehensively took into account all important mechanical and hydraulic factors that affect the stiffness of a hydraulic system, resulting in the examined snaking behaviour. Because of this, it is possible at the design stage to select the optimal parameters of the hydraulic steering system to minimise any adverse influence on the snaking behaviour of articulated frame steer wheeled vehicles. This leads to minimising the number of required corrections and minimising energy losses in this hydraulic steering system. The innovative model presented in the article can be used to optimise positioning accuracy, for example, in manipulators and any mechanical system with hydraulic steering of any system of any mechanical parts.