The zero-stress state of a vein is, like that of an artery, not a closed cylindrical tube, but is a series of segments whose cross-sections are open sectors. An opening angle of each sector is defined as the angle subtended between two radii joining the midpoint of the inner wall to the tips of the inner wall. Data on the opening angles (mean ± standard deviation) of the veins and vena cava of the rat are presented. For the superior vena cava and subclavian, jugular, facial, renal, common iliac, saphenous, and plantar veins, the opening angle varies in the range of 25 to 75 deg. The inferior vena cava (below the heart), however, has noncircular, nonaxisymmetric cross-sections, a curved axis, and a rapid longitudinal variation of its “diameter;” its zero-stress state is not circular sectors; but the opening angle is still a useful characterization. The mean opening angle of the interior vena cava varies in the range of 40 to 150 deg in the thoracic portion, and 75 to 130 deg in the abdominal portion, with the larger values occurring about the middle of each portion. There are considerable length, diameter reductions, and wall thickening of the vena cava from the homeostatic state to the no-load state in vitro. Physically, the zero-stress state is the basis of the stress analysis of blood vessels. The change of opening angle is a convenient parameter to characterize any nonuniform remodeling of the vessel wall due to changes in physical stress or chemical environment. Change of zerostress state influences the compliance and collapsibility of the viens, their pressure-volume and pressure-flow relationships, the waterfall phenomenon, and the tone in the vascular smooth muscles if the homeostatic stress is changed.