This study considers a disaster preparedness and relief distribution problem. The problem is first modeled through a risk-neutral multistage stochastic programming problem, and then the risk-neutral problem is converted to a risk-averse one by adding the so-called chance constraints. Because chance constraints can make the feasible sets non-convex, these chance constraints are further converted into Conditional Value-at- Risk constraints, which are then added to the objective function. The decisions at the first-stage are the locations of the warehouses and their sizes, and the quantities of the emergency items to be pre-positioned at the opened warehouses. The decisions at later stages are the quantities to be purchased to update the inventories of the emergency items and the quantities of these items to be distributed to the disaster victims. It is assumed that the demands for the emergency items and the road capacities are random vectors with known probability distributions and that these random vectors are stage-wise independent. Furthermore, the problem is solved dynamically through the so-called Stochastic Dual Dynamic Programming algorithm, because the initial realizations of the demands and the road capacities are updated during the relief distribution phase. In the solution procedure, the decision process is non-anticipative; that is, the decisions at stage t only consider the realizations of the random vectors up to and including stage t. In the numerical illustrations, the following two questions are investigated: i- What is the impact of risk on the T-stage cost? ii- What is the impact of correlations between the components of the demand and road capacity vectors on the T-stage cost? The results of the numerical illustrations are sound and interesting.