— The rapid transit network design problem considers at upper level the list of potential transit corridors and stations to design the network as a discrete space of alternatives. At lower level the alternatives are evaluated based on the route and mode user decisions. The optimization objective is to maximize the transit demand considering the user’s behaviour and the network design constraints. The stochastic extension considers the demand as a random variable, the formulation considering “a priori” and “a posteriori” models are considered. The model is proved experimenting the formulations using Branch and Bound in test networks.