Computational fluid dynamics is a computer simulation technique used to study the effects of stenosis and aneurysm degree on haemodynamics in the blood vessels such as blood velocity, pressure, and wall shear stress. The current study employed the numerical simulations of pulsed blood flow using the Carreau non-Newtonian rheological and Newtonian models to model the wall shear stresses and haemodynamics in blood vessels. Furthermore, the model included three stenosis areas with different diameters, 70%, 80%, and 90%, and two aneurysm areas with different diameters, 15% and 44%. The study observed the blood velocity, pressure, and wall shear stresses at the damaged blood vessels areas. It was found that the maximum velocity was observed from stenosis when the stenosis ratio was increased to 90%. Additionally, the velocity increased up to 3.4 times, which led to increased blood shear stresses to up to 8.4 times, when the start acceleration flow and peck flow were compared. It is known that the degree of damage on blood vessels produces the most significant influence on local blood pressure and shear stresses. Therefore, it was concluded that stenosis at 90% may probably lead to serious lesions and effectively block the bloodstream by the ensuing thrombus.