Liquefaction of gases is one of the applications of cryogenic science. Among the gases, Helium has the lowest boiling point, which at a pressure of 1atm is approximately 4.2K. Liquid helium can be used to cool superconductors in transportation equipment, military radars, and medical imaging equipment. For helium liquefaction, various cycles are used; these cycles have different parameters in their structure such as of input mass fraction to expanders, heat exchanger effectiveness, expander arrangement and ... which their analysis for improving the performance of the cycle is important. In this research, the aim is to study 2, 3 and 4 expander cycle with various parameters and structure. For...