The responses of a bridge due to a moving vehicle are obtained analytically by modeling a vehicle as a constant point force. From the results it is found that the responses after a vehicle leaves the bridge become very small for some speeds of a vehicle. When a vehicle is modeled as a two dof system for a more accurate analysis, the same phenomenon is observed while the roughness of the surface of the bridge is small. Determining the fundamental frequency of a bridge so that one of the above speeds coincides with a frequent speed of vehicles, the responses of a bridge can be minimized.