Sorption-based compressors are thermally driven and because of the absence of moving parts they are vibration free, and have the potential for long life. Sorption-based compressors have been reported to operate Joule–Thomson (JT) cryogenic coolers with pure working fluids. However, using mixed refrigerants instead of pure refrigerants is attractive since that would dramatically improve the system coefficient of performance. Our on-going research aims to develop an efficient JT sorption cryocooler, operating with mixed refrigerants, and is focused on studying the characteristics of the sorption compressor cycle. This paper presents the results of an advanced numerical analysis, which is based on a previous model, and its experimental verification. The analysis relates to the ideal cycle of a sorption compressor operating with a gas mixture. Obviously, dynamics and kinetics play a major rule in a real sorption compressor cycle. However, since there are no reported gas-mixture sorption compressors and the existing experience in this field is poor, a preliminary ideal cycle analysis is considered. Satisfying agreement between the numerical and experimental results is obtained and the processes in the sorption cycle are discussed. The outcomes of the current study are the basis for the next phase in which a sorption compressor prototype will be built operating with gas mixtures.