It is customary in inventory theory to assume that payments must be paid to the supplier for the items immediately after receiving the consignment. In real business transactions, the supplier allows a certain fixed credit period to settle the account for stimulating retailer’s demand and increasing revenue. From the retailer’s viewpoint, during the credit period before payment must be made, he/she can sell the items and continue to accumulate revenue and earn interest. This article explores an inventory system with nonistantaneous receipt and allowable shortages under conditions of permissible delay in payments. The nonistantaneous receipt model under trade credit is newly introduced. The purpose of this article is to determine the optimal replenishment policies under conditions of nonistantaneous receipt and trade credit. We present an algorithm to find the optimal solutions so that the total relevant cost per unit time is minimized. Numerical examples are presented to illustrate the proposed model.