We compare four approaches to geomechanical modeling of stresses adjacent to salt bodies. These approaches are distinguished by their use of elastic or elastoplastic constitutive laws for sediments surrounding the salt, as well as their treatment of fluid pressures in modeling. We simulate total stress in an elastic medium and then subtract an assumed pore pressure after calculations are complete; simulate effective stress in an elastic medium and use assumed pore pressure during calculations; simulate total stress in an elastoplastic medium, either ignoring pore pressure or approximating its effects by decreasing the internal friction angle; and simulate effective stress in an elastoplastic medium and use assumed pore pressure during calculations. To evaluate these approaches, we compare stresses generated by viscoelastic stress relaxation of a salt sphere. In all cases, relaxation causes the salt sphere to shorten vertically and expand laterally, producing extensional strains above and below the sphere and shortening against the sphere flanks. Deviatoric stresses are highest when sediments are assumed to be elastic, whereas plastic yielding in elastoplastic models places an upper limit on deviatoric stresses that the rocks can support, so stress perturbations are smaller. These comparisons provide insights into stresses around salt bodies and give geoscientists a basis for evaluating and comparing stress predictions.