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The severity of traffic barrier crashes has been modeled in the literature based on human, road, and traffic barrier factors. However, all these factors interact in a complicated way so the relationship between these factors still remains unclear. A structural equation model (SEM) can be used to capture the intricate relationships between the contributory factors and the latent or unobservable factors. This study was conducted using the SEM to model the complicated relationships between the confounding factors and traffic barrier crash severity. Due to possible differences across different road classifications, the SEM was applied separately to the highway and interstate systems. The SEM involves the measurement or confirmatory factor analysis (CFA) model and the structural model involving the interrelationships between the factors. This study evaluates traffic barrier crash severity in terms of numbers of death, injury, and severity of crashes. This study examined the nature and causes of severe traffic barrier crashes in Wyoming. The results indicated that road conditions, traffic barrier types, risky driving, and force are factors that need to be considered in addressing the severity of traffic barrier crashes. The methodology in this study also addresses categorical predictors and model selection techniques for specifying the measurement model and the structural model which make up the SEM. A careful sequential modeling framework was used to build the structural model characterizing the interrelationships among the latent variables as well as evaluation of the fitted SEM based on goodness of fit indices. [ABSTRACT FROM AUTHOR]