In this article, the Robust Vehicle Routing Problem (RVRP) with uncertain traveling costs is studied. It covers a number of important applications in urban transportation and large scale bio-terrorism emergency. The uncertain data are defined as a bounded set of discrete scenarios associated with each arc of the transportation network. The objective is to determine a set of vehicle routes minimizing the worst total cost over all scenarios. A mixed integer linear program is proposed to model the problem. Then, we adapt some classical