The assessment of running safety of railway bridges is conditioned by the Eurocode EN 1990 A2 by limiting vertical deck acceleration. On ballastless track bridges, this value is 5 m/s2. The background for this value is not clear, and it is believed that it originates in the application of an arbitrary safety factor of 2 on accelerations around 1 g to avoid loss of wheel–rail contact. However, studies show that the level of acceleration may not be directly related to the occurrence of derailment. In this work, this idea is expanded by assessing both vertical and lateral dynamics, comparing acceleration values with the Unloading and Nadal derailment criteria. The parametric study is comprised of a set of five representative single-track slab bridges with spans between 10 m and 30 m with two levels of track irregularities, corresponding to a well-maintained track and an Alert limit situation. A three-dimensional articulated FE model based on the load properties of the EN 1991-2 High-Speed Load Model A is presented, crossing the bridges at running speeds from 150 km/h to 400 km/h. Despite the complexity of the models, a large amount (1461) of full 3D train–track–bridge interaction dynamic analyses are performed, to produce a data set representative of the phenomenon. Results show a weak correlation between the criteria and deck acceleration (maximum r2 of 0.47 for Unloading and 0.15 for Nadal). Additionally, track quality is shown to be a more conditioning factor for derailment when compared to resonance. This work contributes to discussing the thesis of using deck acceleration as an indicator of running safety, considering lateral dynamics.