When urgent situations occur (e.g., inaccurate demand forecast, traffic accidents, or infectious disease outbreaks), the stock of rescue medical items in the hospital might not be enough to cater to the drastically increased demand. Comparing with placing an expensive emergent replenishment order with dealers, requesting inventory sharing from another hospital with excessive stocks could save time and cost. This paper investigates the operation of the inventory sharing mechanism between two independent hospitals with the consideration of patient behavior. We first identified the inventory decisions when hospitals are under a no-sharing scenario, and derive hospitals’ sharing policies and inventory policies under the sharing scenario. Through numerical experiments, we found that the inventory sharing option is profitable for hospitals compared to emergent replenishment. Furthermore, we investigated the effects of patient behavior, safety inventory level of the hospital, and other cost parameters on inventory decisions. Under the sharing policy, the increase of hospital j’s emergent request rate and safety inventory level increased the optimal initial inventory level of hospital i, while the increase of hospital j’s initial inventory level decreased the optimal inventory level of hospital i. This paper provides more practical suggestions for hospitals’ inventory sharing operation.