Cryogenic technology is used for liquefaction of many gases and it has several applications in food process engineering. Temperatures below 123 K are considered to be in the field of cryogenics. Extreme low temperatures are a basic need for many industrial processes and have several applications, such as superconductivity of magnets, space, medicine and gas industries. Several methods can be used to obtain the low temperatures required for liquefaction of gases. The process of cooling or refrigerating a gas to a temperature below its critical temperature so that liquid can be formed at some suitable pressure, which is below the critical pressure, is the basic liquefaction process. Different cryogenic cycle configurations are designed for getting the liquefied form of gases at different temperatures. Each of the cryogenic cycles like Linde cycle, Claude cycle, Kapitza cycle or modified Claude cycle has its own advantages and disadvantages. The placement of heat exchangers, Joule-Thompson valve and turboexpander decides the configuration of a cryogenic cycle. Each configuration has its own efficiency according to the application. Here, a nitrogen liquefaction plant is used for the analysis purpose. The process modeling tool ASPEN HYSYS can provide a software simulation approach before the actual implementation of the plant in the field. This paper presents the simulation and statistical analysis of the Claude cycle with the process modeling tool ASPEN HYSYS. It covers the technique used to optimize the liquefaction of the plant. The simulation results so obtained can be used as a reference for the design and optimization of the nitrogen liquefaction plant. Efficient liquefaction will give the best performance and productivity to the plant.