In case of direction-dependent viscoelasticity, a simplified formulation of the three-dimensional quasi-linear viscoelasticity has been obtained manipulating the original Fung equation. The experimental characterization of the static hyperelastic behaviour, the relaxation, the dynamic modulus and the loss factor of woven Dacron from a commercial aortic prosthesis has been performed. An 11 % difference of the reduced relaxation (after infinite time) between axial and circumferential directions has been observed for the woven Dacron. A very large increase in stiffness is obtained in case of harmonic loading with respect to the static loading. These findings are particularly relevant for dynamic modelling of currently used aortic grafts.