The dynamic behavior of a woven Dacron graft, currently used in thoracic aortic reconstructions in the case of aneurysm or dissection, has been experimentally investigated for the first time. Dacron grafts are widely used in cardiovascular surgery to replace segments of diseased large blood vessels; however, scarce data are available about their durability. The dynamic modeling of such prostheses may fill this gap and may provide guidelines for the study of human aortic segments as well. Dynamic phenomena such as vibrations are being included among the most likely causes of important aortic pathologies, such as dissections and consequent ruptures. The compatibility of the dynamic behavior of Dacron grafts and human arteries seems a characteristic worthy of experimental investigation as well. For this reason, a cylindrical Dacron graft has been subjected to fixed boundary conditions and to a physiological value of static axial pre-stretch. A constant internal pressure, equal to the average value of the physiologic blood pressure, was exerted by a liquid mixture of suitable viscosity and density. A three-dimensional quasi-linear viscoelastic model was fitted onto the Dacron fabric by means of dedicated traction and relaxation tests. Forced linear and large-amplitude vibrations were imposed and measured. An identification tool recently developed by this research group is being used to study the change of the equivalent modal damping ratio with vibration amplitude during nonlinear vibrations. Furthermore, an ongoing study is revealing a dependence of dissipation on frequency that is coherent to the most common model for biological materials adopted by the medical community.