Finite element wall stress simulations on patient-specific models of abdominal aortic aneurysm (AAA) may provide a better rupture risk predictor than the currently used maximum transverse diameter. Calcifications in the wall of AAA lead to a higher maximum wall stress and thus may lead to an elevated rupture risk. The reported material, properties for calcifications and the material properties actually used for simulations show great variation. Previous studies have focussed on simplified modelling of the calcification shapes within a realistic aneurysm shape. In this study we use an accurate representation of the calcification geometry and a simplified model for the AAA. The objective of this approach is to investigate the influence of the calcification geometry, the material properties and the modelling approach for the computed peak wall stress. For four realistic calcification shapes from standard clinical CT images of AAA, we performed simulations with three distinct modelling approaches, at five distinct elasticity settings. The results show how peak wall stress is sensitive to the material properties of the calcifications. For relatively elastic calcifications, the results from the different modelling approaches agree. Also, for relatively elastic calcifications the computed wall stress in the tissue surrounding the calcifications shows to be insensitive to the exact calcification geometry. For suffer calcifications the different modelling approaches and the different geometries lead to significantly different results. We conclude that an important challenge for future research is accurately estimating the material properties and the rupture potential of the AAA wall including calcifications.