Following the background of transportation network, this paper considers a transportation network flow problem on the long term (strategic) planning level.Specifically, considering the uncertainties of capacities of links and nodes, we formulate an integer programming model based on the stochastic scenario-based capacity representation and unique solution constraints cross different scenarios.Lagrangian Relaxation solution approach and a genetic algorithm are designed in order to obtain an approximate optimal solution.Finally, the numerical experiments are implemented to demonstrate the efficiency and effectiveness of the proposed approaches.