Although wandering phenomenon of passenger and commercial cars is often experienced on damaged and dented roads, this phenomenon has not been theoretically studied so far. The objectives of this paper are to show, using linear stability theory, how and why the wandering phenomenon occurs. Firstly, the fourth order characteristic equation of a car running on a damaged road surface, taking the cross profile into account, is derived to theoretically analyze the running stability. Secondly, according to root locus analysis of the characteristic equation, it is clearly found that the vehicle body fluctuation on dented roads is much influenced by the forward velocity, the wheel track depth, and the vehicle parameters. Thirdly, a first order preview driver model is introduced to discuss the performance of the closed-loop system of driver-vehicle during lane changes. It is found that it becomes difficult for the driver to control the vehicle when the depth of the dented track increases, which shows a good agreement with the theoretical analysis.