At present, due to the increase in the caterpillar machines power-to-weight ratio, when the technologies for manufacturing highly-engineered engines are known and widely used, the machine average speed following the traction capabilities limitations has increased significantly. Therefore, the motion regime along periodic irregularities is possible, with the caterpillar being completely detached from the supporting surface. This motion type leads to constant incidence of the car from a certain height and frequent suspension breakdown, since the suspension system (SP) is selected according to other criteria. The article considers a method for selecting a damping characteristic that provides the maximum energy capacity while providing a given acceleration level in the driver place. The article shows simulation results, and confirms that the powerful forward damping introduction allows us to suppress the oscillations.