At the present time more and more efficient cryogenic systems, in which use complex schemes and cycles are created. To develop programs for their calculation and optimization, such as cryogenic air separation plants, it is advisable first to carry out computational studies of systems, in which employ a relatively simple scheme and the thermodynamic cycles. Obtained in studies information about more simple objects will be easier to analyze it. The results of the calculation of expander-throttle liquefier unit operating from the known cycle are given. The features of its mathematical model and calculation programs are described. On their basis, the energy and design characteristics of the unit are examined upon transfer in it from the idealized thermodynamic cycle to the cycle, in which are considered the technical losses: incomplete recuperation on by warm end of the heat exchanger precooling air, the heat flows from environment to the devices units, hydraulic resistances and intensity of heat transfer in the straight and return flows. A number of restrictions that follow from the second law of thermodynamics is used in the program. Air is selected as a working body with the pressure of 2 MPa on the outlet of the compressor. The optimum value of air flows through the expander, at which the total surface of the three coils of twisted tubular recuperative heat exchanger reaches a minimum.