How much and how the thrombus supports the wall of an abdominal aortic aneurysm (AAA) is unclear. While some previous studies have indicated that thrombus lacks the mechanical integrity to support much load compared with the aneurysm wall, others have shown that removing thrombus in computational AAA models drastically changes aneurysm wall stress. Histopathological studies have shown that thrombus properties vary through the thickness and it can be porous. The goal of this study is to explore the variations in thrombus properties, including the ability to isolate pressure from the aneurysm wall, incomplete attachment, and their effects on aneurysm wall stress, an important parameter in determining risk for rupture. An analytical model comprised of cylinders and two patient specific models were constructed with pressurization boundary conditions applied at the lumen or the thrombus/aneurysm wall interface (to simulate complete transmission of pressure through porous thrombus). Aneurysm wall stress was also calculated in the absence of thrombus. The potential importance of partial thrombus attachment was also analyzed. Pressurizing at either surface (lumen versus interface) made little difference to mean von Mises aneurysm wall stress values with thrombus completely attached (3.1% analytic, 1.2% patient specific) while thrombus presence reduced mean von Mises stress considerably (79% analytic, 40–46% patient specific) in comparison to models without it. Peak von Mises stresses were similarly influenced with pressurization surface differing slightly (3.1% analytic, 1.4% patient specific) and reductions in stress by thrombus presence (80% analytic, 28–37% patient specific). The case of partial thrombus attachment was investigated using a cylindrical model in which there was no attachment between the thrombus and aneurysm wall in a small area (10 deg). Applying pressure at the lumen resulted in a similar stress field to fully attached thrombus, whereas applying pressure at the interface resulted in a 42% increase in peak aneurysm wall stress. Taken together, these results show that the thrombus can have a wall stress reducing role even if it does not shield the aneurysm wall from direct pressurization—as long as the thrombus is fully attached to the aneurysm wall. Furthermore, the potential for porous thrombus to transmit pressure to the interface can result in a considerable increase in aneurysm wall stress in cases of partial attachment. In the search for models capable of accurately assessing the risk for rupture, the nature of the thrombus and its attachment to the aneurysm wall must be carefully assessed.