This paper describes a mathematical model for the prediction of the dynamic loads induced on a bridge structure by the passage of vehicles: the model is defined in the time domain and represents the bridge and the vehicles as dynamic systems interacting with each other via wheel-road contact forces. The numerical outcomes of the mathematical model are compared to measurements performed on an existing steel bridge, and show satisfactory agreement. The mathematical model was eventually applied to the estimation of load spectra corresponding to daily traffic. In particular the load spectra corresponding to different vehicles and speeds were combined by using a statistical description of the traffic. It is shown that this procedure leads to results very close to the ones measured on the structure.