Woven Dacron grafts represent standard implants for replacements of the thoracic aorta in current medical practice. Wide knowledge about the distinctly different mechanical properties of the Dacron implants with respect to the native aorta is available in literature while very little is known about the dynamic behavior of these prostheses. This study addresses the dynamic response to pulsatile physiological blood flow and pressure of woven Dacron grafts currently used in thoracic aortic replacements. The structural model assumes a cylindrical orthotropic shell described by means of the nonlinear Novozhilov shell theory. Residual stresses because of pulsatile physiological pressurization are evaluated and included in the model. The pulsatile flowing fluid is formulated using a hybrid model that contains the unsteady effects obtained from linear potential flow theory and the viscous effects obtained from the unsteady time-averaged Navier-Stokes equations. Physiological waveforms of blood pressure and velocity are approximated with the first eight harmonics of the corresponding Fourier series. Coupled fluidstructure Lagrange equations for a non-material volume with wave propagation in case of pulsatile flow are utilized. Frequency-response curves in the physiological range show the geometrically nonlinear vibration response to pulsatile flow with several superharmonic resonance peaks in the high physiological frequency range. Different values of modal damping are considered; in the limit case of low modal damping values, flow-induced asymmetric vibration of the aortic prosthesis is possible. Finally, in order to reproduce the weave design of the woven Dacron fabrics, geometric imperfections are introduced in the structural model. The numerical natural frequencies of the pressurized prosthesis are compared with the experimental results obtained from the modal analysis of a woven Dacron graft.