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A novel semi-analytical geomechanical workflow offers a fast and efficient alternative to traditional 3D finite element models for evaluating containment integrity in underground hydrogen storage. Applied to a depleted gas field in the Netherlands, the method uses a nucleus-of-strain approach to estimate stress and deformation responses during hydrogen injection and withdrawal cycles. By slightly simplifying subsurface mechanics, the model enables rapid screening of potential storage sites without compromising the reliability of early risk assessments. Results for this particular case study show that surface deformation remains below 1 cm and that stress changes in the caprock during hydrogen cycling are smaller than those observed during historical gas depletion. The models indicate a low risk of top seal failure during hydrogen storage compared to the gas depletion phase, and the relative increase in shear failure risk during hydrogen injection and production remains within safe bounds. This modeling approach significantly reduces computational cost while providing critical insights into containment risks, making it a valuable tool for early-stage site selection in hydrogen storage development.