An abdominal aortic aneurysm (AAA) is a dilation localized in the infrarenal segment of the abdominal aorta that can expand continuously and rupture if left untreated. Computational methods such as finite element analysis (FEA) are widely used with in silico models to calculate biomechanical predictors of rupture risk while choosing constitutive material properties for the AAA wall and intraluminal thrombus (ILT). In the present work, we investigated the effect of different constitutive material properties for the wall and ILT on 21 idealized and 10 unruptured patient-specific AAA geometries. Three material properties were used to characterize the wall and two for the ILT, leading to six material model combinations for each AAA geometry subject to appropriate boundary conditions. The results of the FEA simulations indicate significant differences in the average peak wall stress (PWS), 99th percentile wall stress (99th WS), and spatially averaged wall stress (SAWS) for all AAA geometries subject to the choice of a material model combination. Specifically, using a material model combination with a compliant ILT yielded statistically higher wall stresses compared to using a stiff ILT, irrespective of the constitutive equation used to model the AAA wall. This work provides quantitative insight into the variability of the wall stress distributions ensuing from AAA FEA modeling due to its strong dependency on population-averaged soft tissue material characterizations. This dependency leads to uncertainty about the true biomechanical state of stress of an individual AAA and the subsequent assessment of its rupture risk.