We compare an evolutionary to a static approach for modeling stress and deformation around a salt dome and we show that the two approaches predict different stress histories and very different strains within the adjacent wall rocks. Significantly higher shear stresses develop during the evolutionary analysis near the base of a rising salt dome. In addition, the static approach is not able to capture the decrease in the minimum principal stress caused by the circumferential dome expansion. Strains predicted by the evolutionary model are an order of magnitude higher than those predicted by the static model, and they show significant shearing in the horizontal plane. The evolutionary approach is performed using Elfen, and the static using Abaqus. Overall, our results highlight that forward evolutionary modeling can capture the stress history of mudrocks close to salt domes, which can improve significantly predictions for material properties (porosity, anisotropy in velocities measurements), as well as pore pressures and shear/tensile strength.