Problem statement. Mobile robots are of significant interest among scientists and designers during the last several decades. One of the prospective drives of such robots is based on pneumatically operated walking (stepping) system with no use of electric, heat, magnetic or other types of energy. This allows the use of pneumatically-driven robots in the cases when the use of other energy sources is prohibited (e.g., in some gaseous or fluid mediums). At the same time, the walking (stepping) type of moving increases the manoeuvrability and cross-country capability of the mobile robot, and decreases the harmful effect of its interaction with the supporting surface (e.g., the fertile soil surface) in comparison with wheeled or caterpillar drives. Purpose. The main purpose of this research consists in substantiation of structure and parameters of pneumatic system of four-degree-of-freedom mobile robot with orthogonal walking drive and turning mechanism. Methodology. The research is carried out using the basic laws and principles of mechanics, pneumatics and automation. The numerical experiment is conducted in MathCAD software; the computer simulation of the robot’s motion is performed using SolidWorks software; the modelling of the pneumatic system operation is carried out in Festo FluidSim Pneumatic software. Findings (results) and originality (novelty). The improved structure of the mobile robot with orthogonal walking drive and turning mechanism is proposed. The pneumatically operated system ensuring the robot’s curvilinear motion is substantiated. Practical value. The proposed design of walking robot can be used while designing industrial (production) prototypes of mobile robotic systems for performing various activities in the environments that are not suitable for using electric power or other types of energy sources. Scopes of further investigations. While carrying out further investigations, it is necessary to design the devices for changing motion speed of the robot and the height of lifting of its feet.