In the current thesis, the Banafjäl Bridge located on the Bothnia line (Botniabanan) in northern Sweden was studied. The bridge is a 40m long composite ballasted high-speed railway bridge. A 3D FE model of the bridge was developed using a commercial FE software, Abaqus. The FE model was calibrated against the measured data of the bridge. The dynamic response of the bridge's FE model was investigated under the dynamic load of the passing HSLM-A train using modal dynamic analysis. The vertical acceleration induced by excitation of the passing train exceeded the permissible limit of 3.5 m/s2 for the speed range of 220-240 km/h. Thus, damping solutions using multiple tuned mass dampers (MTMDs) were investigated. According to the results of this study, a 4 tonnes MTMD system consist of 5 parallel TMDs attached to the mid-span of the bridge could effectively control the undesired vibration of the bridge. The suggested solution could account for the changes in the stiffness of the bridge caused by freezing and ice forming in the ballast.