Abstract: Two models, displacement input model and acceleration input model, for analyzing the structural response of earthquake ground motion are discussed. The direct integration methods in these models are analyzed. It is found that the displacement input model is more accurate than the generally used acceleration input model, given the same direct integration method and time step. This is contrary to the conclusions that there are several sources of numerical errors associated with the direct application of earthquake displacement loading and a very small time step is required to define the displacement record and to integrate the dynamic equilibrium equation. It is believed that the displacement input model is more accurate and suitable for analyzing the seismic responses of structures, especially for the responses of structures subjected to spatially varying ground motion.