A unified method for the production of pure ¹²³I from highly enriched ¹²⁴Xe targets bombarded by photons, protons and helium ion beams is described. A computer code ALICE 85/300, based on the pre-equilibrium hybrid model of nuclear reactions, was used fore the calculation of excitation functions for the ^124,126Xe (p, xnyp) ¹²³Cs->¹²³Xe->¹²³I and ¹²⁴Xe (^3,4He, xnyp) ¹²³Ba->¹²³Cs->¹²³Xe->¹²³I reactions from theresolds up to 120 MeV for proton and 100 MeV for ^3,4He ions. A comparison of calculated cross section with experimental data for the ¹²⁴Xe (p, 2n)¹²³Cs and ¹²⁴Xe (p, pn)¹²³Xe reactions measured in the energy range 16-44 MeV shows good agreement. For the ¹²⁶Xe (p, xnyp) ¹²³Cs->¹²³Xe->¹²³I reaction we expect a similar accuracy. Excitation functions of the ¹²⁴Xe (gamma, n) reactions have been calculated using another computer code (PEQAG), also based on the pre-equilibrium-equilibrium process. Due to the lack of experimental data for photoneutron reactions on Xe targets, we compared the results calculated in the present work with existing experimental data for neighbouring elements of Xe. It has been found that the data for these elements agree well with the present results. The calculated excitation functions for the ¹²⁴Xe (^3,4He, xnyp) ¹²³Ba ¹²³Cs->¹²³Xe->¹²³I reactions are suggested to be used an estimate in the planning of an experiment. This study has arisen from an interest in predicting optimal conditions for production of ¹²³I (needed in nuclear medicine) using one target system connected with cryogenic technique.