Local stress concentrations in some specific geometric details often play an essential role in  time-dependent damage propagation. However, measured strain or stress data are generally available in locations that are not the most critical ones. Proper numerical models are thus required to aid the damage severity assessment. In this paper, a surrogate model procedure based on the local response function method is proposed to accurately predict stress time histories in particular regions of bridges through a multiscale numerical analysis. The methodology is calibrated on the basis of direct strain measurements on a railway bridge in Vänersborg, Sweden. The bridge is currently monitored with a set of strain gauges, accelerometers, and an inclinometer allowing the investigation of its in-service conditions during the train passages and the lifting of the bascule truss. The results show the reliability of the method for stress prediction in specific regions of the bridge without the availability of directly measured data together with more detailed knowledge about the stress histories that could lead to fatigue or corrosion damage.