This study investigates, experimentally and analytically, the polygonal wear of truck/bus and car tires and elucidates the generation mechanism of polygonal wear caused by the first natural vibration mode of the tire in the vertical direction. In the analysis, the phenomenon is modelled as a time delay system accompanied by wear in which the amount of wear of the tire is fed back as forced displacement in the vertical direction after the time period of tire rotation. The progress of the polygonal wear of the tire is very slow and is caused by unstable vibration in the steady-state wear process generated in the limited regions where the products of polygonal numbers and the rotational speed of the tire are less than the natural frequencies of the tire system. The tire is deformed almost to the shape of a regular polygon when polygonal wear occurs. Good agreement between experimental and analytical results concerning the occurrence of polygonal wear of the tire was confirmed.