One of the defining areas for further research in the world is the development of a set of technological measures for the introduction of resource-saving technologies and technical means, ensuring reduction in the need for material, technical and energy resources. The introduction of track and bridge systems in farming, the basis of which is a wide-span bridge traction vehicle, is really promising in this respect. The development of power-driven agricultural axle traction machines brings forward the necessity of setting and solving the problems of uncontrolled (passive) driving with its own tasks and solution methods. The aim of this research is to investigate uncontrolled passive steering of a bridge vehicle with power steering. The methodological basis of the theoretical research was the system approach, mathematical modelling, the laws of theoretical mechanics, the theory of tractors and vehicles, information technology and the use of PCs. A prototype of a wide span vehicle has been used as the object of experimental investigations. As a result of this research, it was found that the maximum value of asymmetrically applied shear pulling force of the wide span vehicle corresponds to the direction when its line of action passes through the centre of mass. For 1 kN of traction resistance of the bridge machine under study, the lateral slip when it moves along the compacted soil track of a constant tramline for each 1 m of the distance travelled was 0.011…0.015 m. In any deviation from this direction, there is an instantaneous rotational movement (shear) of the wide span vehicle where the total shear force is less than the maximum value. The anisotropy of this process results in a reversal of the hodograph towards a lower coefficient of traction of the wide span vehicle thrusters on the bearing surface of the permanent technological track. The adequacy of the meta-mathematical models of the passive steering of the bridge vehicle with the power method of control allows the solution of problems such as calculation of the minimum turning radius, evaluation of the technological track width, calculation of the maximum traction forces, selection of the rational control scheme under steady driving conditions, calculation and reduction of power on the turn, calculation of the maximum dynamic loads at the moment of active driving and others.