Emergencies often lead to the impairment of infrastructure systems, including transportation systems. It is necessary to analyze the uncertainty and correlation of transportation network capacity caused by emergencies, aiming at the problems of emergency facilities’ location and matching in emergency contexts. This study introduces novel concepts, such as flow distribution betweenness centrality (FD-BC) and the transport capacity effect coefficient (TC-EC). Furthermore, we introduce the ellipsoidal uncertainty set to characterize uncertainties in transport capacity. We construct a multi-criteria decision-making (MCDM) model and a multi-strength elitist genetic algorithm (multi-SEGA) to ensure the lower limit of transport capacity between demand and emergency points while minimizing decision-making costs. By designing an uncertain scenario example, we analyze the effect of the perturbation ratio and the uncertainty level on the robust location model. The following results were drawn: (1) Indicators FD-BC and TC-EC effectively indicated the importance of each section in the emergency transportation network. (2) The optimal value of the model’s objective function changed more significantly as the perturbation ratio and uncertainty level increased. (3) After reaching a certain uncertainty level, the robust model with an ellipsoidal uncertainty set became more conservative than the robust model with a box uncertainty set, which lacked practical significance. The research results guarantee the robustness of the emergency support system in uncertain conditions.