Gas hydrate sediments are considered as one of the potential sources of unconventional energy because of their high energy density and presence of abundant subsurface reserves in order to meet the rising global energy demand. Methane gas hydrate sediments generally occur naturally in permafrost regions and in deep-sea continental shelves where the water depth is more than 500 m below the mean sea level. These deep-water sediments have a high concentration of methane hydrates. Efficiently extracting (safe and economical) these unconventional energies will help in mitigating the energy demand of a country. The current study focuses on predicting the geo-mechanical response of gas hydrates using elastic-plastic constitutive relations and compare with the existing elemental experimental results. From the numerical integration of these advanced models, it is observed that the HISS-MH model could simulate realistic material response under triaxial conditions. Further, an investigation is also carried out to understand the effect of hydrate saturation and Over Consolidation Ratio (OCR) on the geo-mechanical response. There is an increase in stiffness, peak stress, stress dilatancy ratio and softening response with the increase in hydrate saturation. The response is due to the enhancement of cementation between soil particles with hydrate saturation. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.