The mechanical properties of a soft tissue are related to its structure. Weshall illustrate this by the properties of the arteries and the lung. Viscoelasticity, strain rate effects, pseudo-elasticity, and constitutive equations ar discussed. The mecahnical properties of an organ is, however, not only based onthe tissues of the organ, but also on its geometry and relationship to the neighboring organs. A typical example is the blood vessel. The capillary blood vessels of the mesentery are “rigid”; those in the bat's wing are “distensible”; whereas the capillaries of the lung are “sheet” like: rigid in one plane, and compliant in another. The stress-strain relationship of the systemic arteries is highly nonlinear, stiffening exponentially with increasing strains; yet that of the pulmonary arteries in the lung is linear. The systemic veins are easily collapsible; yet the pulmonary veins in the lung are not: they remain patent when the blood pressure falls below the alveolargas pressure. The explanation of these differences lies in the varied interactions between the blood vessels and the surrounding tissues in different organs. The implications of these differences on blood circulation are pointed out. Therole of ultrastructure is discussed.