In this study, we consider the supplier selection problem of a relief organization that wants to establish framework agreements (FAs) with a number of suppliers to ensure quick and cost-effective procurement of relief supplies in responding to sudden-onset disasters. Motivated by the FAs in relief practice, we focus on a quantity flexibility contract in which the relief organization commits to purchase a minimum total quantity from each framework supplier over a fixed agreement horizon, and, in return, the suppliers reserve capacity for the organization and promise to deliver items according to pre-specified agreement terms. Due to the uncertainties in demand locations and amounts, it may be challenging for relief organizations to assess candidate suppliers and the offered agreement terms. We use a scenario-based approach to represent demand uncertainty and develop a stochastic programming model that selects framework suppliers to minimize expected procurement and agreement costs while meeting service requirements. We perform numerical experiments to understand the implications of agreement terms in different settings. The results show that supplier selection decisions and costs are generally more sensitive to the changes in agreement terms in settings with high-impact disasters. Finally, we illustrate the applicability of our model on a case study.