SummaryA study about the running safety of trains moving over bridges subjected to earthquakes is presented. The study focuses on moderate earthquakes with relatively small return periods and high probability of occurrence. The analyses are performed using a nonlinear train‐bridge interaction method proposed by the authors, being the running safety evaluated with safety criteria existent in the literature. The influence on the train running safety of the seismic intensity levels, train running speed, and track quality is evaluated. Because no significant nonlinearity is likely to be exhibited in the columns for moderate levels of seismicity, the analyses are performed in the elastic domain. However, the reduction in the columns stiffness due to cracking is accounted, and a methodology to compute their effective stiffness is proposed. Copyright © 2015 John Wiley & Sons, Ltd.