Traditionally, the seismic response analysis of a bridge does not account for the concurrent vehicle-bridge dynamic interaction. However, the behavior of a seismically excited bridge can jeopardize the safety of the vehicles running on it, even if the bridge itself remains undamaged. This study examines the seismic response of a vehicle-bridge interacting (VBI) system under vertical earthquake excitation, modelling the truck vehicles as rigid body assemblies. An application of the proposed scheme to a realistic case of (highway) bridge-(truck) vehicles shows that the earthquake ground motion and the road surface conditions are the main sources of excitation. The results show that the road surface conditions influence strongly the dynamics of the VBI system, even when the vertical component of the earthquake excitation is significant. Also, the study brings forward the influence of traffic parameters (namely the speed, the number and the distance between the running vehicles) and underlines the need to consider different positions of the vehicle/s (on the deck) during the earthquake shaking. Finally, it examines the tendency of the wheels of a truck vehicle to detach (jump) from the deck during the seismic response of the VBI system. Detachment tends to be more frequent as the road surface conditions deteriorate and/or the peak ground acceleration increases. However, detachment is a complicated phenomenon which depends also on many other ground motion and VBI system parameters and deserves further study.