ABSTRACT Excess renewable energy can be used to generate and store hydrogen underground, offering a secure and econimical solution to the intermittency challenges of renewable energy sources. The success of underground storage relies on understanding and controlling the geo-mechanical integrity of storage sites during cyclic loadings. While geological deformation during natural gas and carbon dioxide storage is well studied, few have investigated pore pressure and in-situ stress variations during cyclic loading, which is unique to underground hydrogen storage sites. This paper presents a predictive analytical model for the pore pressure and stress changes during cyclic loading. The model was derived based on continuous point source injection, a basic hydro-mechanical model while applying the superposition to consider the cyclic loading. The developed model was evaluated for hydrogen and natural gas subjected to cyclic injection and production. Comparing hydrogen and natural gas storage cases can offer valuable insights into the behavior of hydrogen since the deformation of natural gas storage is more studied. Finally, analytical solutions for both storage cases were validated by numerical models with discrepancies between the models amounting to less than 1%. Comparative analysis of the results from 3 to 99 cycles of injection and production for both hydrogen and methane demonstrates that rise in cycle numbers leads to a corresponding rise in stress accumulation in the system. Neglecting the stress accumulation during these cycles can lead to significant geomechanical issues, potentially compromising the storage system’s safety and integrity.