Failures of bridges crossing wide rivers may cause a number of inconveniences, such as loss of several lives, damages to public and private properties, and traffic disruption. That is why various modes of bridge failures should be accounted for in the planning and design phases to compensate for such negative impacts. Based on the experience gained from past events, it is known that excessive scouring at bridge piers and abutments has been the main cause of bridge failures. The scouring phenomenon is relatively complex and high degrees of uncertainties are associated with the parameters characterizing this event. Accurate determination of the maximum possible depth of scour at these elements is of importance in realistic decision-making for the safe design of footings. This study is based on the development of clear-water scouring models for bridge abutments having vertical-walls, by using empirical and semi-empirical approaches. The reliability of the abutment footing level is estimated using the empirical model employing Monte Carlo simulations. An application is also presented to illustrate the use of this approach.