A computer model to simulate coronary fluid dynamics has been developed which can give some insight into the role of hemodynamics in health and disease. Although this study focuses mainly on coronary blood flow, the complete model consists of all major branches of the systemic circulation as well as the left epicardial coronary circulation;The flow equations are obtained by integrating the one-dimensional continuity and momentum equations over the cross-section of the artery to give a relationship between the primary variables of interest, the pressure and flowrate. An arctangent model was used as a constitutive equation to describe the pressure-area relationship for the arterial wall. The distal point of each terminal branch is modeled using a lumped parameter impedance to account for all the cumulative effects of the distal vasculature. The systemic circulation terminal impedances each contain a simple constant property modified windkessel. The coronary terminal impedances are modeled using similar lumped parameter models. The first model employed was based on the waterfall concept of collapsible tube dynamics. The second model was slightly more sophisticated and was based on the intramyocardial pump concept. Unlike the systemic terminal impedances, the coronary terminal resistance and compliance values are allowed to vary throughout the cardiac cycle according to the extravascular compressive pressure created by the contracting myocardium. The above system of nonlinear partial differential equations was discretized using a finite difference formulation and solved numerically;Both coronary models developed could predict realistic flow patterns in the epicardial arteries. The computer model is also capable of investigating the effects of coronary stenoses with vascular bypasses on epicardial blood flow. The limitations of the model are mainly related to the assumptions needed to obtain the simplified form of the governing equations and the extensive amount of parameter data that are required. Overall, this type of model offers a useful tool for studying the fluid dynamics of the human circulation.