The conscious sheep is an important large animal model for the study of human cardiovascular and cardiopulmonary system. In this study we develop a closed-loop mathematical model of its cardiovascular system. A distributed approach is taken in describing the systemic circulation, which is divided into cerebral, coronary, foreleg, thoracic, abdominal, and hind-limb circulations. Nonlinear aspects of the systemic venous system are described, which include nonlinear pressure-volume characteristics of small and large veins and pressure-operated valves in large veins. The complete integrated model mimics typical steady-state hemodynamic data in the supine position. It is also used to predict the blood volume shifts and hemodynamic changes that accompany standing up. These include the short-term neurally mediated cardiovascular response to the orthostatic stress. Additional studies predict the circulatory response to an increased afterload (balloon inflation) presented to the right ventricle. This model is further used to predict the response of the ovine cardiovascular system to the implantation of the PAL (Para-corporeal Artificial Lung device and to test the putative effectiveness of different PAL device designs.