The paper analyses a two-stage cascade refrigeration system that finds its application in various refrigeration plants. As an important topic in the field of ecology and sustainability today when it comes to the choice of food, energy, cars, clothing or cosmetics, refrigeration systems are also improving. New types of refrigerants are required, and the Laws regulate the areas of application, production, and use. The task is to calculate a two-stage cooling system that uses R-134a as a working substance in both cascades. The solution of such system is obtained analytically, and the results are presented graphically. The solution was calculated using the Engineering Equation Solver (EES) program. Based on the knowledge of the results from the system with R-134a in the lower and upper cycle, the replacement of the working substance in lower cascade was performed and CO2 is used. The solution of such a system was obtained by the Engineering Equation Solver (EES) program. It is concluded that it is necessary to optimize such a system because the obtained solutions for such a system are different or less than in the original case. After optimization with the Engineering Equation Solver (EES) program and theoretical knowledge, it was concluded that the value of the coefficient of performance (COP) can approach the value of the initial system, but to achieve a better coefficient of efficiency it is necessary to change individual system components and operating conditions.