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A major challenge in network service providers is to provide adequate resources in service level agreements based on forecasts of future demands. In this paper, we address the problem of capacity provisioning in a network subject to demand uncertainty such that a network coded multicast is applied as the data delivery mechanism with limited budget to purchase extra capacity. We address some particular type of uncertainty sets that obtain a tractable constrained capacity provisioning problem. For this reason, we first formulate a mathematical model for the problem under uncertain demand. Then, a robust optimization model is proposed for the problem to optimize the worst-case system performance. The robustness and effectiveness of the developed model are demonstrated by numerical results. The robust solution achieves more than 10% reduction and is better than the deterministic solution in the worst case.