This paper discusses mathematical models for reconstructing pre- and post-impact trajectory phases of vehicular collisions. These models consist of three vehicle dynamic models, a tire traction model and three tire/road coefficient of friction models. The vehicle dynamic models include a two dimensional seven degree of freedom model with constant tire normal loads, a seven degree of freedom model with dynamic tire normal loads, and a three dimensional ten degree of freedom model. The tire traction model presented here, developed by Sakai, is used in all trajectory models. The three tire/road coefficient of friction models discussed are constant, linear and sweeping coefficient of friction models. These trajectory models are then compared with experimental data obtained from a series of violent maneuver tests performed with instrumented passenger cars.AS COMPUTER BASED reconstruction of vehicular collisions becomes more popular, the necessity for accurate analytical models of the pre- and post-impact phases of collisions becomes greater.The models for reconstruction of pre- and post-impact phases of vehicular collisions, referred to as trajectory models in this paper, consist of a vehicle dynamic model, tire traction model and a tire/road coefficient of friction model. Although the coefficient of friction model can be thought of as part of the tire traction model, they are treated separately in this work. Tire traction models are mathematical models relating the interaction between the tire and road surface at the contact patch. They are used to determine the cornering and braking forces as well as the self aligning moment generated as a result of this tire/road interaction.First, the three vehicle dynamic models are discussed. Next, the three coefficient of friction models and the tire traction model are presented. After the description of the violent maneuver tests, three of the tests and their computer simulations are presented. Finally, the conclusions are presented.