In this study, a theoretical model is established using Engineering Equation Solver (EES) software in order to investigate the effects of different design and operation parameters on the performance of the cascade systems for Ultra Low Temperature (ULT) between -50 degrees C and -100 degrees C. The analysis is performed for natural and synthetic refrigerant pairs to find an environmentally friendly alternative to commercial synthetic refrigerants. Effects of common parameters such as the evaporation temperature of low temperature cycle (LTC), the condensation temperature of high temperature cycle (HTC) and the temperature difference in the cascade heat exchanger (HX) have been investigated with the proposed model. Furthermore, influence of operation parameters including vapor quality of the refrigerant after the expansion valve and the precooler heat exchanger (PCHX) capacity, crucial to reach ULT conditions, on the system performance are examined. This study also contributes to the theoretical evaluation of the feasible natural refrigerant alternatives for ULT applications and the comparison of these refrigerants with synthetic ones in terms of performance and the environmental aspects. It is found that the natural refrigerant R1270/R170 pair results in about 5% better COP and almost half less CO2 emissions compared to synthetic refrigerant R404A/R508B pair.