The flow of blood through a rigid artery with different degrees of stenosis has been studied. Two different shapes (rectangular and cosine) of stenosis are considered while blood is modeled either as a Newtonian or non-Newtonian fluid. Three different degrees of stenosis, expressed in percentage, are considered representing mild to severe stenoses. The flow separates from the arterial wall at the stenosis and reattaches at a point downstream, forming a recirculating eddy. The pressure drop over the length of the artery varies for the different cases indicating the impact on the heart. A peak in the wall shear stress is observed at the location of the stenosis and zero stress points are observed where the flow separates and reattaches the wall. Results show marked differences in the flow pattern and shear stress between Newtonian and non-Newtonian models. Moreover, the power-law model exhibits a different trend as compared to the Casson model in predicting the flow field and wall shear stress.