Long-duration energy storage using hydrogen can play a major role during India’s transition from a fossil fuel-based economy to a green energy economy and change India into a self-sustained energy export economy from a major energy import economy. We need a long-duration energy storage system to improve the use and reliability of intermittent renewable energy. Due to the large gravimetric energy density and very small volumetric energy density, it is required to compress hydrogen and store it in a tank or underground cavern for further use in the transportation and industrial sectors. However, hydrogen can be stored in gas, liquid, and solid states. Hydrogen in gaseous form stored at very high pressure, i.e., 25, 35, and 70 MPa, is the most promising solution for transportation applications. This paper presents a comprehensive exergy analysis of multistage hydrogen compression and storage. Several parameters, including isentropic efficiencies of the compressors, pressure ratio, pressure in the storage vessel, preset pressure inside the storage vessel, etc., are considered in this analysis. This analysis has yielded significant insights pertaining to exergy destruction, exergy efficiency, and loss in power happening to the irreversibility of various parts/components of the system. The obtained results demonstrate that the amount of exergy destroyed and, thus, the compressor’s exergy efficiency, is significantly affected by the working pressure ratio and the compressor’s isentropic efficiency. The analysis found that the increase in storage pressure usually causes an improvement in the exergy efficiency of all three compressors. When the compressor is operating at low isentropic efficiency, η is equal to 0.70, the improvement becomes more apparent. For the low value of preset pressure inside the vessel, i.e., 10 MPa, more exergy is stored during storage of the hydrogen gas at max pressure, i.e., 70 MPa. For the storage process, it has been observed that the exergy destruction is mainly affected by the preset pressure inside the storage tank, and it can be minimized by using an isobaric filling process. The mechanical exergy stored in the hydrogen gas during isochoric storage at 700 bar is 380.49 MJ/m3.