The report analyzes and selects the liquefaction cycle for Liquid Air Energy Storage. The specific liquefaction coefficient and the coefficient of thermodynamic perfection were calculated for the following cycles: the Linde-Hampson cycle, the Claude cycle, the Heylandt Cycle, the Collins cycle, and the cycle with two expanders. The criterion for optimizing cycles is the maximum value of the liquefaction coefficient. The Claude cycle was chosen as the optimal cycle for use in the Liquid Air Energy Storage. Its exergy efficiency was calculated.