Roadway intersections are crash-prone locations and, hence, ensuring the safety of road users at intersections has been a major concern for transportation professionals. It is critical to identify the risk factors that contribute to severe crashes at intersections to implement the appropriate countermeasures. Greater emphasis is needed on two-vehicle crashes since they represent the majority of intersection crashes. In this study, a random parameter ordinal probit model was developed to estimate the contributing factors of injury severity of two-vehicle crashes at intersections. Nine years of intersection crash data in Wyoming were analyzed in this model. The study involved the investigation of the influence of a set of intersection, drivers, environmental, and crash characteristics on crash injury severity. The results demonstrated urban and signalized intersections were related to lower severity levels. In addition, higher pavement friction is more likely to be associated with less severe crashes. Crashes that involved drivers who are females or impaired and crashes on weekends were associated with higher severity levels. Intersection crashes that occurred on non-dry road surfaces, in adverse weather conditions, or that involved large vehicles, or out-of-state drivers were less likely to be severe.