We use a fully coupled poroelastoplastic geomechanical model to study how stresses and pore pressures evolve in sediments bounding a spherical salt body. Drained analyses (pore pressures remain hydrostatic) demonstrate that sediments yield in response to loading by the salt, which leads to a redistribution of stresses and to deformations larger than predicted by poroelastic or solid Coulomb-plastic models. Undrained analyses (overpressures develop while no dissipation occurs) illustrate that salt loading induces pore pressures that extend kilometers away from the salt body. We also model the flow and consequent dissipation that occur in the sediments because of this undrained salt loading. We show that with time, the pressure field dissipates and expands. The dissipation process takes millions of years, which suggests that pore-pressure perturbations caused by salt loading should still be present in mudstones near many salt bodies. Under drained conditions, stress perturbations generate low minimum principal stresses above and below the salt, resulting in convergence of pore pressure and minimum principal stress at these locations. Such conditions are challenging to drill through. In undrained systems, sharp drops in pore pressure may occur above and below the salt, whereas both the pore pressure and the minimum principal stress rise next to the salt. In contrast to previous models that do not couple changes in stress to changes in pore pressure, the coupled approach presented here has the potential to predict in-situ stresses and pore pressures more accurately in a wide variety of geologic settings.