Since the effect of magnetic fields on blood flow is not fully understood or studied comprehensively, this paper, for the first time, addresses the effect of uniform magnetic fields with different intensities on the pulsatile non-Newtonian blood flow in an elastic artery with axially symmetrical single and double stenoses using the commercial software COMSOL Multiphysics 5.1. The results are suggestive that an increase in the percent stenosis increases the pressure drop, which is more dramatic in double stenosis. Moreover, for a given percent stenosis, increasing the Hartmann (Ha) number, in addition to increasing the pressure drop, increases the amount by which the pressure drop is raised. The shear stress results revealed that increasing the magnetic field intensity results in the reduction of the vortex region formed in the back of the stenosis, reducing the area prone to disease, which can resolve pathological issues. The impact of the magnetic field was found to be decreased by increasing the percent stenosis. It was also observed that the percentage difference between the maximum wall shear stresses for various percent stenoses is reduced by increasing the Ha number for both single and double stenoses.