The lateral dynamic behaviours of a track inspection vehicle with laterally guided system are studied for the safety and comfort. A 10-DOF dynamic model is proposed counting for lateral and yaw motions. The equations for motions of the vehicle running on curved tracks at a constant speed are presented. It is shown by simulation that lateral guiding forces applied to the guiding wheels on the inner side of the track increase in a larger scale in comparison with those on the outer side when the vehicle passes through curved tracks with cant, and the front guiding spring forces is larger than the rears. Lateral vibrations due to yaw motions of the vehicle take place when the vehicle runs through curved tracks. Finally, effect of the lateral guidance on the vehicle dynamics is also examined and advantages of such a guiding system are discussed in some details. An optimal guided control is applied to restrain the lateral and yaw motions. The comparisons between the active and passive guidance explain the effect of the active control approaches.