Earlier experimental work on decellularized arteries revealed the existence of significant residual stresses within the arterial wall, which are released upon chemical removal of vascular smooth muscle in normal arteries causing substantial radial expansion. Hence, the often-used Hill's model describing active and passive stresses within the wall does not hold true, because the existence of prestresses precludes the fundamental assumption of zero active stress when the vascular smooth muscle is inactive. We have, therefore, developed a new mathematical model based on a modified Hill's model, where the total wall elastin is partitioned in two parts: one in-parallel to vascular smooth muscle and collagen and one connected in-series with vascular smooth muscle. Based on experimental evidences, compressive prestresses were assumed to exist on the parallel elastic component and tensile prestresses on the series elastic component. Further, we assumed that the elastic constants of elastin and collagen and the statistical description of collagen engagement are not affected by decellularization. Excellent fits of the pressure-diameter curves of normal and decellularized arteries were obtained. The model predicts that the majority of elastin is in-series with the vascular smooth muscle (74 +/-8%) and thus only about one-fourth of elastin acts in parallel to the vascular smooth muscle. We conclude that correct biomechanical modeling of the arterial wall requires the knowledge of the zero stress state of both the series and parallel elastic components.