Carotid artery stenosis (CAS) can have a variety of shapes at the stenosis region. Generally, the severity of CAS is judged by the blockage percentage regardless of stenosis shape. However, certain studies on coronary artery stenosis suggest that the shape of stenosis significantly affects the various hemodynamic parameters due to altered flow structures arising as the shape of stenosis changes. Hence, a comparative study is carried out comparing two different stenosis shapes namely eccentric and axisymmetric stenosis for CAS in internal carotid artery. We observe significant variations of flow structures as the shape of stenosis changes. These variations in flow structures lead to higher time-averaged wall shear stress (TAWSS) for eccentric stenosis compared to axisymmetric stenosis. Hence, eccentric stenosis is much more susceptible to plaque rupture than axisymmetric stenosis with the same blockage.