This paper develops a new model for studying multiechelon inventory systems with stochastic demand. For the model we assume that each site in the system orders at preset times according to an order-up-to policy, that delivery times are deterministic, and that the demand processes are stochastic with independent increments. We introduce a new scheme for allocating stock in short supply, which we call virtual allocation and which permits significant tractability. We exercise the model on a set of test problems for two-echelon systems to get insight into the structure of good policies. The primary findings are that both the central warehouse (upper echelon) and the retail sites (lower echelon) should hold safety stock, but that most of the safety stock should be at the retail sites. Consequently, the central warehouse will stock out with high probability. Furthermore, we show that the virtual allocation rule is near optimal for the set of test problems.