Characterising circulatory dysfunction in critically ill patients, and choosing a suitable treatment, is a difficult and time-consuming problem often faced by medical staff. A stable, minimal closed loop model of the human cardiovascular system (CVS) is developed with the specific aim of assisting medical staff in understanding, diagnosis and treatment selection. Models found in the literature simulate specific areas of the CVS with limited direct use to medical staff while others are either overly complex, difficult to solve, and/or unstable. This thesis develops a minimal model with the primary goal of accurately capturing dynamic trends in the entire CVS. Focus is not just on the overall structure, but on the individual components, such as elastic chambers and fluid flow elements, to ensure their physiological accuracy. A novel mixed-formulation approach to simulating blood flow in lumped-parameters CVS models is outlined that adds minimal complexity, but significantly improves physiological accuracy. Optimisation is used to determine patient specific model parameters and create patient specific models in reasonable times, taking the model closer to useful clinical application than previous models. The minimal model is shown to match experimentally measured static and transient CVS dynamics for ventricular and cardiopulmonary interactions. Few other models are verified to simulate dynamic cardiopulmonary interactions, and none were found that simulate dynamic ventricular interactions. The minimal model was also verified to simulate a variety of CVS dysfunctions due to heart disease and shock. By simulating different dysfunctions and reflex responses, the model can be used to improve understanding of the major contributing factors to CVS dysfunction as well as the relative importance of specific elements and reflex actions. The model offers a powerful tool that can be used in conjunction with experimental research to improve understanding of CVS function, and assist medical staff in diagnosis and therapy selection.