Comparison of stress relaxation following sudden volume increase of isolated segments of carotid and umbilical arteries indicates that tension contributed by the smooth muscle component disappears in a few sec., leaving only the tension contributed by elastic components. The time course of stress relaxation in the arterial wall is non-exponential, and can be resolved only when residual stress is plotted vs. log time. This behavior is discussed in light of existing theories of similar behavior in artificial materials.