A deterministic inventory model with two levels of storage (own warehouse and rented warehouse) for non-instantaneous deteriorating items with stock dependent demand is studied. The supplier offers the retailer a trade credit period to settle the amount. Moreover, shortage at Own Warehouse (OW) is also allowed subject to partial backlogging. The backlogging rate varies inversely as the waiting time for the next replenishment. Different Cases based on the trade credit period have been considered. The objective of this work is to minimize the total inventory cost and to find the optimal length of replenishment and the optimal order quantity. Computational algorithms for this model are designed to find the optimal order quantity and the optimal cycle time. The solution methodology provided in this model helps to decide the feasibility of renting a warehouse and to avail a trade credit period. The results have been elucidated with numerical examples. Numerical illustrations and managerial insights obtained demonstrate the application and the performance of the proposed theory.