•A realistic theory for damped vehicle moving over simple bridge.•Derive a new procedure for calculating the contact point (CP) response.•Being free of vehicle frequency, CP response is good for obtaining higher bridge frequencies.•CP response is less affected by vehicle damping compared with the vehicle response.•Ongoing traffic is positive to deal with the negative effect of road roughness. By the vehicle scanning method, an instrumented test vehicle is used to scan the frequencies of vibration of the underlying bridge. In this paper, a realistic theory is proposed considering the damping effect of the test vehicle, which was not well studied previously. Bridge damping is ignored since the bridge vibration sensed by the moving vehicle is transient in nature. The vehicle response was criticized for the presence of vehicle frequency, which renders "scanning" less effective. In contrast, the response of the vehicle's contact point (CP) with the bridge is free of the vehicle frequency and enables us to extract more bridge frequencies. For the model adopted, closed-form solutions are firstly derived for both the vehicle and CP responses, with their transmissibility discussed. Through the numerical simulations and field test, the following are concluded: (1) The improved procedure for the CP response is reliable for scanning the first few bridge frequencies; (2) the effect of vehicle damping on the CP response can be ignored; (3) the performance of the CP response is always better than the vehicle response for each scenario studied; and (4) ongoing traffic is a positive effect that can outbalance the negative effect of surface roughness. Display omitted