Due to its less harmful impact on the environment compared to coal and oil, and certain political and social factors, the demand for gas is expected to grow in the coming years. In gas demand, oscillations occur due to different climatic conditions in winter and summer and also people's way of life. Therefore, it is reasonable to use facilities such as gas storage facilities, which can cover daily and seasonal fluctuations in demand. Storages can be aboveground and underground. In this paper, the project of the peak underground gas storage "Grubišno Polje" is observed, the construction of which is in progress. In the Grubišno Polje field, two exploration wells gave a positive result on the existence of natural gas. In the first phase of the project, this gas will be partially depleted and compressed into the gas transport system of the Republic of Croatia. After depletion phase, the partially depleted reservoir will be used to temporarily store gas from the system. For the processes of initial gas extraction and its injection, a compressor driven by a gas engine is used. The working volume of the reservoir will be about 100 million m3, and it will be characterized by relatively large capacities of gas injection and withdrawal, which will cover the peak loads in the system and security of gas supply in the Republic of Croatia. The mathematical model will first describe the phase of extraction of gas, and then the process of injecting gas from the main gas pipeline into the reservoir, which begins the phase of gas storage. The model also describes the phenomena in the compressor, which allows to determine the dependence of the required power of the gas engine on the filling of the tank. Also, as part of the mathematical model, a comparison of storage operation is given through two scenarios with different levels of tank filling. When the tank filling level is high, the gas pressure also reaches high values, so withdrawing such gas means energy loss. The reason for the loss is that high-pressure gas must not be allowed into a gas pipeline whose pressure is significantly lower, and it is necessary to reduce it. Also, more gas engine power is required to inject gas into a tank whose charge level is high.