We consider capacity expansion of a telecommunications network in the face of uncertain future demand and potential future failures of network components. The problem is formulated as a bicriteria stochastic program with recourse in which the total cost of the capacity expansion and the probability of future capacity requirements to be violated are simultaneously minimized. Assuming the existence of a finite number of possible future states of the world, an algorithm for the problem is elaborated. The algorithm determines all non-dominated solutions to the problem by a reduced feasible region method, solving a sequence of restricted subproblems by a cutting plane procedure. Computational results are reported for three different problem instances, one of which is a real-life problem faced by SONOFON, a Danish communications network operator.