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Arterial hypertension is a prevalent condition and a major risk factor for cardiovascular and neurological diseases. Notably, medical treatment fails to control blood pressure in a large proportion of diagnosed subjects, highlighting gaps in our understanding of hypertension's pathophysiology. Using a mathematical model of the human cardiovascular system, we quantify the contributions of various cardiovascular compartments to the hypertensive state. The impact of uncertainty in modelling assumptions is assessed through stochastic modelling. Our results show that reduced venous vascular compliance significantly increases arterial pressure, making it the second most influential factor in determining hypertension, after increased peripheral resistance. KEY POINTS: We used a closed-loop mathematical model of the full human circulation to simulate adaptation to hypertension, including stochastic variation in parameters. The model quantifies the relative importance of different cardiovascular parameters in determining arterial pressure. Venous compliance emerged as the second most influential determinant of arterial pressure, after systemic resistance. Reduced venous compliance alone was sufficient to cause a hypertensive state in the model. These findings highlight the potential of the venous system as a novel therapeutic target for blood pressure regulation.