Static and dynamic analysis of a circular cylindrical shell that models a segment of human aorta is carried out in this study. The shell is assumed to have three hyperelastic layers with residual stresses. Material data and residual stresses are taken from the literature from human toracic descending aorta. The material model is the Holzapfel-Gasser-Ogden (HGO). Dissipation is modelled by viscoelasticity. The dynamic load is given by a pulsating pressure reproducing the physiological pressure during the heart beating. The inertial effect of the contained blood fluid is taken into account. Under the static pressure, the initially soft shell becomes much stiffer, which is a common feature of soft biological tissues. The nonlinear dynamics is not particularly complicated, due to the significant damping.