The structure of a long curved girder bridge is represented with a three-dimensional curved finite element model. Each 4-axle vehicle is modeled by a dynamic system of 35 degrees of freedom. The random irregularities of the track are generated from a power spectral density function under the given track condition. The dynamic interaction between the bridge and train is realized through the contact forces between the wheels and track. Then based on these models, the coupled equations of motion are solved by applying the time-integration and iteration techniques to the coupled system. The proposed formulation and the associated computer program are then applied to a real curved girder bridge. The dynamic responses of the bridge-vehicle system and the derailments and offload factors related to the riding and running safeties of vehicles are computed. The results show that the formulation presented in this paper can well predict dynamic behaviors of both bridge and train with reasonable computation efforts.