One expression of the fact that real arteries, in the physiological range, are not simple elastic tubes is expressed by increase of its stiffness at greater pressures. Let stiffness G be defined as rate of change of arterial pressure P with size V, i.e. dP/dV, where V stands for volume or cross-section area or diameter, relatively to a reference value. It has been shown that G(P) = β(P+α), where β and α are pressure-independent constants and β (‘stiffness index’) measures the rate of stiffness increase per one unit of pressure change. Both parameters can be determined by measuring stiffness at different pressures. This equation is identical to the so-called Tait equation (Tait, 1888) that describes the ‘equation of state’ liquids (P-V relationship over thousands of atmospheres) with remarkable accuracy. Although at elevated pressures liquids are compressed while arteries are stretched, in both cases the constituting components change its packing under pressure. This suggests using the knowledge accumulated in high-pressure physics for interpreting stiffness-related measures in arteries. Following this approach it can be shown that arteries behave as elastic tubes only for size changes ΔV<<1/β -a condition that is violated frequently during the systole; the known increase of β with age and vascular pathology may reflect ‘enhanced structuring’ of the wall components; The parameter α may stand for ‘internal pressure’ contributed, in part, by the net attraction/repulsion of wall elements, independently of the applied pressure. In conclusion, stiffness-related measures may probe the physical state of the arterial wall microstructure.