Isotopic enrichment by low-temperature distillation of carbon monoxide is difficult to handle, the experiments providing with the necessary data are time-consuming and difficult to perform, so the mathematical modeling of the process is an appropriate approach to study and to further control the column. This paper develops a mathematical model for the (C-13) isotope cryogenic distillation process using two subsystems of the plant: the hydrodynamic part and the isotope-separation part. The model is validated using experimental data from the pilot column from the National Institute for Research and Development of Isotopic and Molecular Technologies Cluj-Napoca. The proposed model is suitable for various cryogenic distillation columns, using the proper parameters.