Automated storage and retrieval systems (AS/RSs) are material handling systems that are frequently used in manufacturing and distribution centers. The modelling of the retrieval–travel time of an AS/RS (expected product delivery time) is practically important, because it allows us to evaluate and improve the system throughput. The free-fall-flow-rack AS/RS has emerged as a new technology for drug distribution. This system is a new variation of flow-rack AS/RS that uses an operator or a single machine for storage operations, and uses a combination between the free-fall movement and a transport conveyor for retrieval operations. The main contribution of this paper is to develop an analytical model of the expected retrieval–travel time for the free-fall flow-rack under a dedicated storage assignment policy. The proposed model, which is based on a continuous approach, is compared for accuracy, via simulation, with discrete model. The obtained results show that the maximum deviation between the continuous model and the simulation is less than 5%, which shows the accuracy of our model to estimate the retrieval time. The analytical model is useful to optimise the dimensions of the rack, assess the system throughput, and evaluate different storage policies.