In this paper presents an analysis of the thermodynamic cycles the most commonly used for the liq uefaction of gases in order to evaluate and compare their performance under given working conditions and system component efficiencies. The cycles considered are simple Linde Hampson cycle, precooled Linde Hampson cycle, Claude cycle, and Kapitza cycle. Fi rst and second law relations are investigated for each cycle and performance parameters are evaluated. Thermodynamically performances criteria are compared of cycles with respect to the each other. Cycles are model in the computer environment and analyzed with Engineering Equation Solver (EES) software program. Cycles of the liquefaction fractions, coefficient of performances and second law of efficiencies are calculated for the liquefaction of different gases. Second law efficiencies are calculated as 13.4 %, 21.8%, 62.9%, and 77.2% for simple Linde Hampson cycle, pre cooled Linde Hampson cycle, Claude cycle, and Kapitza cycle, respectively. Claude and Kapitza cycles give better performance but simple and precooled Linde Hampson cycle has the advantages of t he simplicity of their setup.