Understanding rock mechanical time-dependent plastic deformation enables the researchers to accurately predict rock responses during loading and unloading. This research focuses on the geomechanical aspects of hydrogen storage, particularly rock resistance to creep deformation under varying stresses and pressures. Modelling creep deformation in underground storage mediums has been overlooked and requires further consideration, as it is a critical, cyclical, time-dependent phenomenon essential for hydrogen containment. The study's novelty is demonstrated in its focus on geomechanical properties of rock minerals, providing insights that aid in site-selection criteria for hydrogen storage A creep deformation model with varying mineral compositions is used to assess creep deformation strain. In homogenous cases, calcite showed the highest resistance to creep deformation after three loading cycles, primarily due to its high Young's Modulus. As for the heterogenous cases, the results indicated that the mixture of calcite and quartz was the most creep-resistant rock composition. In terms of rock types, basalt samples demonstrated the highest resistance to creep deformation, while siltstone exhibited the highest susceptibility to deformation. It was observed that as the number of cycles increase, the rock mechanical stability decreases, hence optimizing the number of cycles is a must to ensure hydrogen geo-containment.