A mathematical model of blood flow through a stenosed artery is presented. The arterial wall and stenosis are assumed to be viscoelastic and axisymmetric. The constitutive equations are solved using pertubation methods and these solutions are compared with the predictions of models that assume Poisseuille and turbulent flow through a rigid stenosed tube. This solution is used to investigate the stress caused by viscoelastic deformation of the wall and the stenosis.