Emergency disaster managers are concerned with responding to disasters in a timely and efficient manner. We are concerned with determining the location and amount of disaster relief supplies to be prepositioned in anticipation of disasters. These supplies are stocked when the locations of affected areas and the amount of relief items needed are uncertain. Furthermore, a proportion of the prepositioned supplies might be damaged by the disasters. We propose a two-stage robust optimization model. The location and amount of prepositioned relief supplies are decided in the first stage before any disaster occurs. In the second stage, a limited amount of relief supplies can be procured post-disaster and prepositioned supplies are distributed to affected areas. The objective is to minimize the total cost of prepositioning and distributing disaster relief supplies. We solve the proposed robust optimization model using a column-and-constraint generation algorithm. Two optimization criteria are considered: absolute cost and maximum regret. A case study of the hurricane season in the Southeast US is used to gain insights on the effects of optimization criteria and critical model parameters to relief supply prepositioning strategy.