When a global pandemic of infectious diseases occurs, demand for medical supplies such as masks, disinfectants, and personal protective equipment will exceed the production capacity in normal times, consequently leading to serious shortages. Stockpiling is necessary to prepare for such situations. However, because pandemics are infrequent and might occur at any time, stockpile freshness is an important concern. As described in this paper, a “rolling stockpile” of medical supplies is proposed to prevent the medical supply stockpile from becoming too old. A formulation of a model and simulations based on it is presented. Results demonstrate that the method is applicable to the design of warehouses for rolling stockpiles, monitoring stockpile depletion during emergencies, and monitoring the process of recovery from emergencies.