In this paper, we study the effect of leadtime information sharing on the safety stock costs of a two-layer downstream supply chain. We focus on a specific pharmaceutical supply chain, in which the shortage can generate the important negative consequences. Considering the uncertainty of lead time and the drastic rules for availability of products, the safety stock represents an important fraction of stock (sometime equal to turnover quantity). We assume that the demand at the retailer (hospital pharmacy) is determinist but the replenishment leadtime at the warehouse (central pharmacy) is variable with uniform distribution. The results of both mathematical demonstration and simulation experimentations show a significant system costs reduction up to 25% due to information sharing.