The efficient and effective response to disasters critically depends on humanitarian supply chains (HSCs). HSCs need to be flexible to adapt to uncertainties in needs, infrastructure conditions, and behavior of other organizations. The concept of 'network flexibility' is, however, not clearly defined. The lack of an unanimous definition has led to a lack of consistent understanding and comparisons. This paper makes a threefold contribution: first, it defines the concept of network flexibility for HSC in the context of sudden onset disasters. Second, it proposes a framework to measure network flexibility in HSCs. Third, we apply our framework to the 2015 Nepal earthquake case and provide evidence-based insights regarding how humanitarian organizations can improve network flexibility in HSCs. Our analyses for Nepal case show that delivery, IT support, and fleet criteria have the most influence on flexibility. Also, the application of our framework on the downstream network of nine humanitarian organizations shows low levels of network flexibility in all but one. This finding explains why several disruptions happened in relief distributions during the Nepal response.