In the cardiovascular diseased (CVD) conditions, it is essential to choose a suitable rheological model for capturing the correct physics behind the hemodynamic in the multiply afflicted diseased arterial network. This study investigates the effect of blood rheology on hemodynamics in a blood vessel with abdominal aortic aneurysm (AAA) and right internal iliac stenosis (RIIAS). A model with AAA and RIIAS is reconstructed from a human subject’s computed tomography (CT) data. Localized mesh generation and pulsatile inflow condition are considered. Non-Newtonian models such as the Power-law, Carreau, Cross, and Herschel Berkley models are used in simulations. The outcome from a validated computational model is compared with the Newtonian model to identify the suitable model for dealing with pathological complications under consideration. The capabilities and significance of various rheological models are also examined via Wall Pressure (WP), Wall Shear Stress (WSS), velocity, Global non-Newtonian importance factor (I_G), Vorticity Streamlines, and Swirling Strength. It is noted that during the entire cardiac cycle, the I_G factor of the cross model is found to be relatively more significant. Power Law depicts larger I_G factor during peak systole and early diastole. Also, the cross model depicts larger WSS, WPS, swirling strength distribution and vorticity during the peak systolic and diastolic phases It is noted that I_G ∼0.02 is an appropriate non-Newtonian blood activity cut-off value in the descending abdominal artery having AAA and RIIAS. The critical important WSS values are in the range of 0–9 Pa which is stated in WSS contour plot.