At the time of natural disasters occurrence, prompt responding and providing required items to affected areas is the most urgent priority. Moreover, given a stochastic nature of the crisis severity and the number of the affected areas,effective planning is a crucial task. In this study, two major steps in the disaster management cycle,namely preparation and response phases, are formulated using a multi-objective mathematical model under uncertainty. In the preparation phase, the optimum location of relief distributions, medical centers and inventories of relief goods to storage items received from suppliers are determined. Also, in the second step or response phase, the amount of relief goods transported from supply points to relief distribution centers and from these centers to affected areas as well as the number of injured people transferred to medical centers and hospitals through ambulances and aerial transportationare determined. Moreover, regarding the problem nature, its key parameters (e.g., demand and the number of injured people) are considered to be uncertain. Furthermore, given that the failureof facilities in both supplier and distributor sections can adverselyaffect their service provision, this issueisconsidered in the model. To efficiently solve the model, the non-dominated sorting genetic algorithm II (NSGA-II) and the multi-objective grey wolf optimizer (MOGWO) areused. Comparison of the results obtained from the proposed meta-heuristics with the exact solution method indicates that these algorithms can provide acceptable solutions in a reasonable amount of computational time.