Over the past decade, all-terrain-vehicles (ATVs) became a popular form of off-road recreational riding. Unfortunately, a large number of ATV accidents occurred causing incapacitating injuries and deaths to riders, many of whom were children under the age of 16. Although statistical data show that these vehicles are extremely dangerous, little engineering information is available to explain how these ATV accidents occur or why the accident rate is so high. Thus, a need exists to know more about the dynamic behavioral characteristics of ATVs so that the public understands more fully the ATVs' lethal dangers and so that the designs of future ATVs are safer;The purpose of this research is to develop a more thorough understanding of the dynamic behavioral characteristics of ATVs. To accomplish this, several new mathematical models of ATV systems are developed. The new models allow for (1) the ATV to have either three or four wheels, (2) the rider to move relative to the ATV, and (3) the ATV system to be operated over a general three-dimensional ground profile. These models are used to determine some of the similarities and differences between the three- and four-wheeled ATVs and the effects that a movable rider can have on the handling and stability of ATVs when operated over various ground profiles. The computer simulation results of these models are compared with each other and to the results of a benchmark rigid rider ATV model;The development and simulation of these new ATV models provides a mechanism for studying the operational characteristics of ATV systems. The results obtained provide a better understanding on how these vehicles should be designed to improve their overturning stability and what riders should do to control these vehicles in avoidance maneuvers. This information will be useful in efforts to reduce the number of serious accidents which occur.