Simplicity and high efficiency of a wheeled mover as a mechanism for converting rotational motion into a translatory one have conditioned its wide application in overland machines including motor vehicles. However a wheel with a non-pneumatic tyre (NPT) has a sufficient drawback lying in termination of a wheeled machine movement at the excess air pressure loss. Moreover, the loss of excess air pressure in a pneumatic tyre of traditional design at high speed of movement of a motor vehicle can lead to a traffic accident with heavy consequences. The stop of a motor vehicle to change a wheel on a heavy traffic roadway or roadside also poses a threat. These reasons determine the necessity of both well-known design improvements and search for the new wheeled mover design solutions to enhance a motor vehicle safety, the use of wheels with non-pneumatic tyres of elastic polymeric materials being one of them. Safety enhancement by means of non-pneumatic tyre use along with keeping the high performance of wheeled machine operational properties, is an important scientific and technical task that determines the research urgency.