In this paper, we present a modelling framework for patient flow in a healthcare system using semi-open queueing network models, which introduces a total bed constraint, above which new patients will be refused admission. Hence this model provides a realistic representation of a real system. This approach enables us to have access to a range of established methods that deals with queueing network models. We demonstrate the usefulness of the model in the context of a geriatric department and show that hospital managers can use this model to gain better understanding of the dynamics of patient flow and to study potential long-term impacts of policy changes.