•Novel fragility models for scoured-critical bridges exposed to multiple hazards were generated•Rigorous FEM included the water-soil-bridge interaction under flooding and earthquakes•Failure modes for bridge components exposed to floods were described•Insights on the flood vulnerability of integral and bridges with bearings are provided•Consideration of uncertainties in scour formation enhance the reliability of risk assessment Building resilient bridges, that are able to withstand multiple natural stressors with minimal damage and quickly restore their functionality is paramount to delivering climate-resilient transport infrastructure. Nevertheless, bridges are proven to be vulnerable to natural hazards, with floods and earthquakes being the main causes of failure. The available research and practice for assessing the vulnerability of river-crossing bridges is predominantly qualitative and therefore relies heavily on visual inspections, while ignoring important characteristics of the complex water-soil-bridge interaction. This is a knowledge gap that this paper aims to fill. This work provides novel fragility models for hydraulically induced stressors and/or combinations of hydraulic and seismic hazards. To achieve this, unique detailed two- and three- dimensional numerical models are employed, for a typical three-span prestressed box-girder river-crossing bridge. This paper is a primer on the vulnerability of flood-critical bridges as it models the entire water-soil-bridge system, taking into account critical hydraulic stressors (scour, debris accumulation, hydraulic forces), the uncertainty in scour hole formation, and all components of integral and isolated bridges: deck, bearings, piers and abutments, backfill, and the foundation soil. A detailed description of the damage modes for each component is given and sets of fragility curves for floods and combinations of hydraulic stressors and earthquakes are developed. The study concludes that integral bridges are in most cases more vulnerable to local scour than bridges with bearings, since the latter are more flexible and can therefore adapt to changes in their geometry. The opposite is true for global scour and/or seismic earthquake excitations. The generated fragility models are useful tools for quantitative risk assessment of transport systems and provide practical means in resilience-based asset management by owners and operators of transport infrastructure.