Abstract The lack of an accurate equation of state for predicting the thermodynamic properties of materials in a wide range of temperature and pressure caused the researchers study on new equations. . In this investigation, a reverse Brayton cryocooler was simulated as a system that prepares the sub-cooled liquid nitrogen supplying the operation condition for high temperature superconductor cables. A computational code was developed for predicting thermodynamic properties of Helium and Neon using fundamental equation of state. Comparing the results with experimental data validate the accuracy of these equations in predicting the thermodynamic properties. Then, using the developed computational code, a reverse Brayton cycle with 10 kW cooling capacity, was designed and simulated and the effect of various parameters on its performance was evaluated. Performance characteristic curves were plotted to illustrate the sensitivity analysis under different operation conditions, and the influence of various parameters such as compression ratio in compressor, maximum pressure, working fluid, efficiency of the heat recovery exchanger and efficiency of expander on the performance of the cycle was addressed. The results showed that the use of neon as a refrigerant gives a better performance than helium. Efficiency of heat recovery exchanger has a significant effect on the performance of cycle, so that 3 percent increase of this parameter increases 11 percent figure of merit (FOM) of the cycle.