Stress-relaxation tests were performed at successive strain levels on strips of human aorta, skin, psoas tendon, dura mater, and pericardium. The elastic fraction, the equilibrium force divided by the initial force, was calculated at each strain increment. In the aorta, the elastic fraction decreased with strain and was modeled as the transfer of stress from elastic to collagen fibers, while in skin it increased with strain, probably due to the rearrangement of individual collagen fiber orientations, resulting in an aligned collagen network at high strains. The strain-independent elastic fractions for tendon, dura mater, and pericardium were similar, and approximately equal to the values found for aorta and skin at high strains. It was hypothesized that the elastic fraction is related to the type of fiber loaded, and the tissue geometry. This analysis may be useful in studying disease-induced changes in the mechanical properties of connective tissues.