It is hard to directly establish the joint probability distribution function of the basic components in the aqueduct system because of the correlation of seismic demand among components in structural vulnerability analysis. A new method for analyzing the vulnerability of the aqueduct structure is proposed. A two-dimensional Copula function is introduced to describe the related structures of component seismic demands and simplify the modeling process of the joint distribution function. First, the vulnerability curves of a bent and rubber bearing are created based on the analysis of time history on a cross of an aqueduct. The independent variable is the peak ground acceleration, and the damage index is the displacement ductility ratio of bent and the deformation of rubber bearing. The uncertainty of ground motion and structural parameters is considered. Second, the vulnerability curve of the aqueduct system is established using the Copula function. Finally, the upper and lower bounds of the aqueduct system vulnerability are obtained by the first-order boundary method. The results show that the failure probability calculated based on the Copula function is between the upper and lower bounds of the first-order boundary method. The results help to simplify the modeling process of the aqueduct system vulnerability curve, and at the same time, providing a new way to study the correlation between seismic demand of aqueduct components.