The traffic congestion is growing in urban area these days. This is because the number of the automobiles is increasing rapidly. To solve this problem, there are many solutions. One of them is to increase the flow rate of a particular traffic artery. A converse approach to increase the flow rate is to make the vehicle smaller and narrower. We developed a new conceptual Narrow Tilting Vehicle (NTV) that has one front wheel and two rear wheels. Also, it is very narrow and all three wheels can tilt to improve the stability during turning. In this paper, we derive a new switching dynamical model of NTV. This model considers several NTV states including normal running, temporary running with one rear wheel not on the ground and totally falling down. Based on this model, a simulation platform is established, which is useful to test different control methods and to investigate dangerous driving situations in case hurt drivers in real experiments. The effectiveness of proposed dynamical model is verified through comparison study of simulations and corresponding experiments.