An emerging copula-based methodology is used to address endogeneity in models of crash injury severity. Specifically, two important sources of endogeneity are addressed: (a) endogeneity due to correlations between the injury severity of the two drivers involved in two-vehicle crashes and (b) endogeneity of collision type and injury severity outcomes. Two sets of copula-based joint model systems are formulated and estimated by using data on two-vehicle crashes from the 2007 Generalized Estimates System: a copula-based joint ordered logit-ordered logit model of injury severities of the two drivers involved in two-vehicle crashes and a copula-based joint multinomial logit-ordered logit model of collision type and injury severity outcomes of two-vehicle crashes. The model estimation results and elasticity estimates underscore the importance of accommodating endogeneity in models of crash injury severity. The results shed new light on the determinants of injury severity in two-vehicle accidents.