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Piers and bearings influence each other in earthquakes, and the failure of any component will affect the whole function of bridges. Thus, it is critical to consider the correlations between multiple components in the seismic vulnerability analysis of the overall bridge system. In this paper, a method of overall seismic vulnerability analysis with nested copula model was proposed to model the correlations between multiple components. The components were combined according to their types to construct the hierarchical structure of the system. The correlation of components was modeled with copula functions, and the nested copula model of the system was eventually developed. Maximum likelihood estimation and goodness-of-fit test were used to select and optimize the copula functions. The overall seismic vulnerability of the multispan bridge system was established using the nested copula model. A four-span continuous rigid frame bridge was used to illustrate the application of the proposed method. The results show that the nested copula model accurately simulated the correlations between multiple components, which would eliminate the overestimation or underestimation by the first-order boundary method. [ABSTRACT FROM AUTHOR]