For the past several years, various simulations of the blood glucose regulatory system have been performed. Mathematical models of such a system have enabled data reduction, diagnostic classification, hypothesis testing and design of critical experiments. These mathematical models, which simulate the behavior of the real physiological systems, are in turn simulated using various digital and analog computer techniques. A single basic model relating blood glucose and plasma insulin has been shown to adequately describe responses of the glucose regulatory system to various challenge stimuli. Specific examples discussed included responses to an oral glucose tolerance test and an intravenous insulin infusion test. The significance of the model conformations to such tests is discussed in view of the goals of modeling and the extension of knowledge of blood glucose dynamics. Although this model is a highly oversimplified representation of the physiological control system, it has been used successfully in a variety of applications.