This paper examines the formulation and solution of the discrete version of the stochastic Network Design Problem (NDP) with incorporated network travel time reliability requirements. The NDP is considered as a two-stage Stackelberg game with complete information and is formulated as a combinatorial stochastic bi-level programming problem. The current approach introduces the element of risk in the metrics of the design process through representing the stochastic nature of various system components related to users’ attributes and network characteristics. The estimation procedure combines the use of mathematical simulation for the risk assessment with evolutionary optimization techniques (Genetic Algorithms), as they can suitably address complex non-convex problems, such as the present one. The implementation over a test network signifies the potential benefits of the proposed methodology, in terms of intrinsically incorporating stochasticity and reliability requirements to enhance the design process of urban road networks.