In this paper, one-dimensional Herschel-Bulkley fluid flow through a stenosed artery, has been studied. The problem is investigated by a joint effort of analytical and numerical techniques. Analytical expressions for several flow variables are obtained. This model has been used to study the influence of the fluid behaviour index n, shear-dependent non-linear viscosity k and the yield stress ô_H in blood flow through a stenosed artery. The variations of axial and plug velocities, flow rate, wall shear stress and pressure gradient with n, k and ô_H, have been shown graphically. It is observed that axial velocity and flow rate increase with slip but decrease with yield stress and, wall shear stress increases in Herschel-Bulkley fluid in comparison with corresponding Newtonian fluid. Biorheological implications of the present modelling for some arterial diseases, are included in brief.