Bridge piers embedded in a riverain region are commonly supported by pile foundations. This provides a flexible restraint to the bridge pier instead of a theoretical rigid foundation type. In this work, a cylindrical bridge pier with a monopile foundation is introduced as an example. A modeling framework is proposed to investigate the dynamic response of bridge piers to the impact of flash flooding. The fluid-structure interaction is directly investigated via a two-way fluid-structure coupling approach and the p-y springs distributed over the interface between the soil and pile are adopted to model the lateral restraints from the soil. The effect of the soil-structure interaction (SSI) on the structural dynamic response is investigated on the basis of 3D numerical models with and without a pile foundation. Moreover, the soil around the pile foundation is vulnerable to erosion by flood flow. This continuous exposure of the pile foundation reduces the lateral load bearing capacity and consequently increases the dynamic responses of bridge structures to flash flooding. To demonstrate the effects of increased exposure of bridge pile foundations on structural dynamic responses, several different scour depths with scour ratios ranging from 0 to 0.5 are included in the numerical analysis. Two different considerations of the pile bottom are included in this study: completely fixed and only vertically fixed. The behavior of bridge piers subjected to flash flooding is thoroughly analyzed, and the damage mechanisms for these two foundation types are investigated. The relationships between peak responses and fundamental periods are determined via regression analysis.