— Dual-failure scenarios are a real possibility in today’s optical networks and it is becoming more and more important for carriers and network operators to consider them when designing their networks. In this paper, we develop and analyze a linear programming model to design a p-cycle network to meet a user-specified minimum dual failure restorability. Results show that p-cycle networks designed for single-failure restorability only exhibit some inherent dual-failure restorability, and that explicitly providing dual-failure restorability is less costly in more richly connected networks.