This study presents a numerical investigation of pressure solution creep and its influence on the mechanical behavior of salt caverns for underground hydrogen storage. A 3D modeling framework, implemented in the open-source simulator SafeInCave, incorporates both dislocation and pressure solution creep mechanisms and is applied to caverns with varying geometries, depths, temperatures, and interlayer positions under realistic conditions. The creep models are appropriately calibrated against experimental results from the literature to account for both stress and temperature effects. Results show that pressure solution creep becomes increasingly significant over time, particularly in shallow and cold formations, where it dominates deformation. It is more active away from cavern walls, where stresses and temperatures are low, while dislocation creep concentrates near the cavern walls and governs behavior at greater depths and higher temperatures. Overall, the study demonstrates that accurately capturing the effect of pressure solution creep is essential for reliable prediction of deformation and structural integrity in underground hydrogen storage caverns.