Aortic stiffness is a major cause of age-related increase in arterial pulse pressure (PP) and associated increase in work load for the heart. A method to treat this condition is proposed: wrapping the ascending aortic wall with a highly compliant elastic material such that reducing the vessel diameter will shift the pulsatile load from the aortic wall to the wrap, thus increasing the functional compliance of the ascending aorta and decreasing the cardiac load. A multibranched mathematical model of the arterial system, in which every segment of the arterial tree is represented as a uniform elastic circular tube, has been used to simulate the effect of the wrapping procedure on PP and impedance changes, by varying the radius (R) and the stiffness (E) of the ascending aortic segment. The results of the simulation show that PP decreases with an increase in R and a decrease in E. A similar trend, but with a different sensitivity, is observed for the characteristic impedance (Zc) changes. The model shows that PP in the ascending aorta can be lowered by 8.8% by reducing R of 20% and decreasing the functional E by 80%, in good agreement with preliminary results obtained from an in vitro pilot study of elastic wrap in aortas. In conclusion, the modelling study demonstrates that the proposed aortic wrapping procedure is able to compensate for the increase in PP associated with R reduction by a decrease in PP determined by a reduction in functional E. Therefore, it supports the use of the aortic wrap as a potential non-pharmacological treatment of age-related increase in PP.