AbstractDue to the extensive development of high-speed railway lines which are operating at increasing velocities, the dynamic performance of railway bridges has become an important issue of scientific research. The aim of this study is to investigate the possibility of reducing the vertical acceleration and displacement of pre-stressed reinforced concrete bridges beams by using passive nonlinear viscoelastic dampers to retrofit them. The proposed solution is based on connecting the dampers directly to the abutments and the bottom surface of the bridge deck with an eccentricity between the neutral axis of the bridge and the contact point of the viscoelastic dampers. First, the dampers are modeled through the concept of linearized fractional derivatives to obtain energetic equivalent linear viscoelastic dampers. Optimization of the configuration of these dampers was performed then as function of the orientation angle and the eccentricity. Considering two bridges having different length that were studied in the literature with other systems of damping, it was found that the best orientation angle of dampers is close to 60°. It was found also that, in order to satisfy Eurocode 1 requirements, the total equivalent damping coefficient for the actual damping system is less than half of that required for systems using auxiliary beam to fix dampers, which indicates higher efficiency of the proposed solution.