A three-dimensional dynamic interaction model is developed for a LIM (linear induction motor) train and elevated bridge system, which is composed of a LIM-driven vehicle submodel and a finite element bridge submodel. Each LIM vehicle is modeled by a 27 degrees-of-freedom dynamic system. The expressions for the electromagnetic force between the linear motor and the reaction plate are derived, and the force model is established. By applying a modal superposition technique to the bridge submodel and using the measured track irregularities as the self-excitations of the train-bridge system, the equations of motion are established for analyzing the dynamic responses of the LIM vehicle and the elevated bridge. The proposed framework is applied to a 3-span elevated bridge with 29.9 m simply-supported girders. The full histories of the LIM train traversing the bridge are simulated, from which the dynamic responses of the LIM vehicle and elevated bridge system are obtained. The proposed method may help to find a way to assess the dynamic properties of elevated bridges and the running safety of a LIM train with reasonable computational effort.