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This chapter proposes a probabilistic framework for assessing seismic and scour effects on existing river-crossing bridge structures. The emphasis is on bridge structures in rural areas, for which it has been recognized that a large number of rural bridges have unknown foundation types and further are subject to both flooding-induced scour and seismic damage. With a review of the US-based rural bridges, this chapter presents a probabilistic framework for bridge performance assessment. Using a representative rural bridge model, the fragility results for the bridge reveal that scour tends to be beneficial in reducing structural damage at slight to moderate seismic intensities and to be detrimental in increasing collapse potential at high-level intensities. The demand hazard curves further quantify probabilistically the occurrence of local damage and global collapse, and systematically reveal the complex effects of scour as a hydraulic hazard on bridge structures.