Experimental evaluations and comparisons of the passive and active biomechanical properties of isolated blood vessels from different species (dog, pig, calf, human), as well as the nature of different arterial pressure oscillations, reveal that: 1) Characteristic impedance of middle-size and large arteries changes with intraluminal mean pressure usually resulting in a U-shaped function with a minimum value around the normal physiological 100 mmHg pressure; 2) Similarly, pressure dependent adrenergic diameter responses (active strain) of different large arteries also exhibit parabolic shape with an extreme (maximum) value at 50-100 mmHg intraluminal pressure, suggesting that biomechanical characteristics of the vessel wall may define an optimum for hemodynamic operations; 3) Changes in the arterial smooth muscle tone shift the characteristic impedance curve along the pressure axis and alter the slopes of the parabola; 4) There are significant interactions between the fast 1st-order (pulsatile) and the slow 3rd-order arterial pressure wave components. These and some other characteristics of the circulatory system suggest the existence of an "extremal" forced oscillation blood pressure control mechanism in the body, optimizing the afterload of heart and the blood perfusion of systemic microvessels by minimizing the pulsatile energy expenditure at the physiological mean pressure operation level. A versatile mathematical model of this hypothetical mechanism was developed by us on an IBM PC using Pascal and 8086 Assembly languages. Simulation experiments show that such a physiological adaptive system could control arterial pressure effectively. The computer model is available on a PC disc.