Accident prediction models are often used to predict the number of accidents on segments and at intersections in the road network. Most often the models are developed for a total number of crashes for the facility, or crashes by severity. However, the frequency and severity of crashes of different types can be expected to vary with regards to the underlying phenomena that cause them to occur. To better account for this variation, this paper describes modeling of accidents at intersections on rural four-lane highways in California separately for four different collision types: Opposite direction crashes, Same direction crashes, Intersecting direction crashes and Single vehicle crashes. The findings from this modeling are reported with a special focus on the differences among crash types with regards to: 1) severity distribution, 2) the dependence on traffic flow, and 3) which variables are best at explaining between site variations in the occurrence of different crash types. There are evident differences in severity as well as the relationship of flow among several of the crash types. Intersecting and Opposite direction crashes are more severe than Same direction crashes. Same and Opposite direction crashes exhibit similar relationships with traffic flow, but there are differences compared to Intersecting direction crashes as well as to Single vehicle crashes. Also the variables that turn out as good predictor variables differ somewhat for each crash type.