The gas dynamic characteristics of 8 single-stage centrifugal compressors of turboexpander units have been approximated with great accuracy by the equations of the new version of the mathematical model of the Universal Modeling Method and have been included in the database of model stages. The universal set of empirical coefficients of the model is somewhat modified for each of the compressors, whose dimensionless gas-dynamic characteristics lie within a fairly wide range. The families of characteristics are calculated by varying the similarity criteria for compressibility. The influence of surface roughness has been investigated, revealing the presence of self-similarity according to the Reynolds criterion. The loss coefficients of the impeller, the vaned diffuser and the exit nozzle are given for two model stages. The database and computer programs of the Universal Modeling Method make it possible to use the characteristics of model stages for designing compressors by the method of approximate gas dynamic similarity.