The aim of the work is to develop a mathematical model which has capability to analyses the design parameters as a function of operations conditions for single and multi-stage Joule Thomson Cryocooler System JTCS. The operations conditions are inlet and outlet pressure, precooling temperature, and mass flow rate. The design parameters are expansion device (length, diameter, and Joule Thomson coefficient), heat exchanger (length, diameter, and effectiveness) and gas type (nitrogen, oxygen, and argon). Theoretical results for nitrogen, oxygen, and argon at initial pressure of 25 MPa, initial temperature of 20ºC, indicate that the final temperature equal to (-16.46ºC, −37.34ºC and −56.75ºC) respectively at single stage JTCS. It also shows the possibility of decreasing the final temperature to (-194ºC, −180.9ºC and −183.8ºC) respectively at multistage JTCS. The experimental rig has been constructed for satisfying mathematical model. The experimental results for nitrogen gas show a temperature drop of 6.5ºC when the initial pressure and temperature were 3 MPa and 20ºC respectively. Theoretical results were validated using experimental measurements on the other hand. The computer program has been built to carry out the analysis required for solving the parameters of JTCS under different operations conditions with good agreement compared to recent published researchers.