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To increase resilience in supply chains, we investigate the optimal design of flexibility in a backup system. We model the dynamics of disruptions as Markov chains, and consider a multiproduct, multisupplier supply chain under dynamic disruption risks. Using our model, we first show that a little flexibility in the backup system can go a long way in mitigating dynamic disruption risks. This raises an important and fundamental question in designing flexibility in the backup system: to achieve the benefits of full backup flexibility, which unreliable suppliers should be backed up? To answer this question, we connect the supply chain to various queueing and dam models by analyzing the dynamics of the inventory shortfall process. Using this connection, we show that backing up suppliers merely based on first moment considerations such as their average reliability or average product demand can be misleading. All else equal, it is better to back up suppliers with (1) longer but less frequent disruptions, and (2) lower demand uncertainty. In addition to such second moment effects, by employing the Renyi’s Theorem, we demonstrate that when disruptions are relatively long (if they occur), backing up the suppliers for which the expected wasted backup capacity is minimum provides the best backup flexibility design. We also develop easy-to-compute and yet effective indices that (a) guide the supply chain designer in deciding which suppliers to backup, and (b) provide insights into the role of various factors such as inventory holding and shortage costs, purchasing costs, suppliers reliabilities, and product demand distributions in designing backup flexibility.