River bridges experience more inconvenient conditions due to the structure-flow interaction compared to bridges having no contact with flow. Therefore, one of the most important components of the bridge failure risk is the risk induced by soil-flow interaction. In this study, the uncertainties of the hydrological and hydraulic parameters affecting the scouring around bridge piers are examined using appropriate probability density functions. In the analyses, the uncertainties involved in the temporal variation of clear water scouring mechanism are considered. Influences of general bed degradation of the main channel and the contraction scour are ignored. The risk associated with the scouring around piers is estimated using Monte Carlo simulations. In the model, the scouring risk of the bridge pier is determined for the given flow, pier geometry and bed material characteristics. The developed model is presented with an example.