This paper deals with the sizing of telecommunications networks offering private line service to a few clients. The clients ask for some transfer capacity between some pair of nodes, but their demand is uncertain. In case of high demand and insufficient capacity, some clients may be denied the transfer; the telecommunications company pays a penalty cost for that. The network has a fixed topology. In planning the network capacity, the company wants to balance the investment cost with the total expected penalty cost. The planning situation is modeled as a stochastic programming problem. The scenarios are built under the assumption that the clients have independent demands. The solution method is based on Benders decomposition coupled with the analytic center solution method. We solve some large size problem instances. For one problem instance, we perform sensitivity analysis and draw the trade-of cost curve vs. the unitary penalty cost. Finally, we run the algorithm on a parallel computing platform.