Accident risk has been applied extensively in transportation safety analysis. Risk is often used to describe the level of safety in transportation systems by incorporating a measure of exposure, such as traffic flow or kilometers driven. The most commonly applied definition of accident risk states that risk is a linear function of accidents and traffic flow. This definition, however, creates problems for transportation systems that are characterized by a nonlinear relationship between these variables. The primary objective of the original research was to illustrate the application of accident prediction models (APMs) to estimate accident risk on transportation networks. (APMs are useful tools for establishing the proper relationship between accidents and traffic flow.) The secondary objective was to describe important issues and limitations surrounding the application of APMs for this purpose. To accomplish these objectives, APMs were applied to a computerized transportation network with the help of EMME/2. The accident risk was computed with the traffic flow output of the computer program. The results were dramatic and unexpected: in essence, the individual risk of being involved in a collision decreases as traffic flow increases. The current and most common model form of APMs explains this outcome. The application of these results may have significant effects on transportation policy and intelligent transportation system strategies.