We consider the capacity planning of telecommunications networks with linear investment costs and uncertain future traffic demands. Transmission capacities must be large enough to meet, with a high quality of service (QoS), the range of possible demands, after adequate routings of the traffic on the created network. We use the robust optimization methodology to balance the need for a given QoS with the cost of investment. Our model assumes that the traffic for each individual demand fluctuates in an interval around a nominal value. We use a refined version of affine decision rules based on a concept of demand proximity to model the routings as affine functions of the demand realizations. We then give a probabilistic analysis assuming the random variables follow a triangular distribution. Finally, we perform numerical experiments on network instances from Survivable fixed telecommunication Network Design Library (SNDlib) and measure the quality of the solutions by simulation. Copyright (c) 2013 Wiley Periodicals, Inc. NETWORKS, Vol. 62(4), 255-272 2013