AbstractConsider a network with arcs subject to failures. We show how the problem of investing in new arcs in such a network in order to increase the expected max flow as much as possible can be formulated as a stochastic program with network recourse. We show how to decompose the problem, and consider both exact methods and approximations. Convergence proofs are given. We demonstrate that max flow recourse problems can be solved very efficiently, since lower and upper bounds are equally simple to evaluate.