A traditional formulation of analytical inventory models does not consider a dependency between sales volume (market demand) and the customer service level provided. The additional assumptions make analytical solutions more complex. Inventory management under service dependent market demand is one of practical problems of that kind. The service dependent demand creates dynamic dependencies between itself and inventory management decisions. A simulation-based approach to managing inventory system under service dependent demand is elaborated in this paper. The appropriate hybrid simulation/analytical model has been developed for dealing with that problem. The modelling of inventory systems under service dependent demand is expanded by considering multi-period stohastic problems. Experimental studies conducted with the model are used to test the ability of traditional inventory systems to meet service level requirements in case of service dependent demand and to identify properties of such systems.