The asserted dominant role of the kidneys in the chronic regulation of blood pressure and in the etiology of hypertension has been debated since the 1970s. At the center of the theory is the observation that the acute relationships between arterial pressure and urine production—the acute pressure-diuresis and pressure-natriuresis curves—physiologically adapt to perturbations in pressure and/or changes in the rate of salt and volume intake. These adaptations, modulated by various interacting neurohumoral mechanisms, result in chronic relationships between water and salt excretion and pressure that are much steeper than the acute relationships. While the view that renal function is the dominant controller of arterial pressure has been supported by computer models of the cardiovascular system known as the “Guyton-Coleman model”, no unambiguous description of a computer model capturing chronic adaptation of acute renal function in blood pressure control has been presented. Here, such a model is developed with the goals of: 1. representing the relevant mechanisms in an identifiable mathematical model; 2. identifying model parameters using appropriate data; 3. validating model predictions in comparison to data; and 4. probing hypotheses regarding the long-term control of arterial pressure and the etiology of primary hypertension. The developed model reveals: long-term control of arterial blood pressure is primarily through the baroreflex arc and the renin-angiotensin system; and arterial stiffening provides a sufficient explanation for the etiology of primary hypertension associated with ageing. Furthermore, the model provides the first consistent explanation of the physiological response to chronic stimulation of the baroreflex.