Arterial stenosis is a common arterial disease and a leading cause of death in the world. The effects of exposure to magnetic fields in stenosis patients are not well known or are not completely investigated. Considering the contradictory results in the literature, the effect of a uniform magnetic field with different intensities on pulsatile laminar/turbulent and non-Newtonian blood flow passing through an elastic conduit with different percentages of stenosis was examined in this thesis. Finite element software including COMSOL multi-physics 5.1 and Adina 8.8 were used for simulations. Results showed that the standard k-? turbulence model is suitable for simulating turbulent flow, while the Careau model is suitable for simulating non-Newtonian blood. Results showed that increased Hartmann number increased the axial pressure drop, which was higher in simple stenosis compared to double stenosis; higher in higher stenosis percentage compared to lower percentage; and higher in the non-Newtonian case than in the Newtonian case. It was also observed that increased magnetic field increases the radial velocity so as to maintain a uniform mass flow. Increased magnetic field also reduced the reverse flow area that is prone to disease, which was more evident in the double stenosis compared to the single stenosis. Wall shear stress magnitudes showed that increased magnetic field increases the maximum artery wall shear stress, which was more pronounced in lower stenosis percentages. The effect of increased magnetic field on shear stress was more evident in the non-Newtonian case compared to the Newtonian case. Keywords: Uniform magnetic field; Pulsatile flow; Lorentz force; Elastic channel, non-Newtonian fluid; ADINA; COMSOL