The principle of moving a hydraulic drilling platform is described. To study the dynamics of transient response processes of hydraulic drive for leveling, a mathematical model was created. The structural diagrams of mathematical models of the actuator and hydraulic control valve are given. The time dependences of the spool positions of the hydraulic control valve and the hydraulic cylinder rod are presented. The dependences of pressure changes in the rod and piston cavities of the hydraulic cylinder are presented.