Abstract For the commercial viability of a hydrogen-based transportation, hydrogen infrastructure is key. One of the major issues of hydrogen infrastructure is related to the deployment and costs of the Hydrogen Refuelling Stations (HRSs), where up to 40% of the cost is related to hydrogen compression. The introduction of Metal Hydride Hydrogen Compressors (MHHCs) in the HRSs as compression elements is a potential technology to reduce operational costs, ensure noiseless operation and increase efficiency, if renewable-based thermal energy (and/or industrial waste heat) is supplied to the system. In this work, four different two-stage MHHCs are introduced and examined in terms of compression ratio, hydrogen flow rate (compression duration), thermal energy requirements and efficiency. In addition, for comparison purposes, a three-stage MHHC is also studied. The properties of five different materials are used for the individual compression stages of the MHHCs, where all the necessary thermodynamic properties are extracted experimentally and incorporated in a commercial Multiphysics software. The unsteady heat and mass transfer equations are employed for the development of the numerical model. The hydrogenation/dehydrogenation kinetics and the temperature profile were validated against solid experimental results. In addition, to improve and accelerate the storage/release kinetics, an internal thermal management scenario has been introduced. The results show that for compression at the temperature range of 10–90 °C, the most favourable two-stage compression case (Case 3) showed a compression ratio of 11.18 ÷ 1, an isentropic efficiency of 4.54% with a thermal energy demand of 322 kJ/molH2 and a cycle time of almost 34 min.