Vascular prostheses used for repairing and replacing damaged and diseased the thoracic aorta in cases of aneurysm, dissection or coarctation have distinctly different mechanical properties than the native aorta. Very little is known about the dynamic behavior of vascular prostheses that can cause unwanted hemodynamic effects leading to their failure. In this study, a Dacron reconstitution of the aorta is modelled as an isotropic cylindrical shell by means of nonlinear Novozhilov shell theory. A numerical bifurcation analysis employs a refined reduced order model to investigate the dynamic behavior of a pressurized Dacron aortic replacement conveying blood flow. A pulsatile time-dependent blood flow model is considered in order to study the effect of pressurization by applying physiological waveforms of velocity and pressure during the heart beating period. Stresses due to pressurization are evaluated and included in the model. The fluid is modeled as a Newtonian pulsatile flow and it is formulated using a hybrid model that contains the unsteady effects obtained from the linear potential flow theory and the pulsatile viscous effects obtained from the unsteady time-averaged Navier-Stokes equations. Geometrically non-linear vibration response to pulsatile flow is here presented via frequency-response curves and time histories. This study provides a fully coupled fluid-structure interaction model and it allows deep insights in the mechanical loading condition of the aortic replacements; this insight has potential to aid in vascular prostheses design and implementation.