The iodine isotopes of 123 I and 124 I with half lives of 13.2 hours and of 4.2 days respectively are commonly used in nuclear medicine and are becoming more widespread recently. The isotope of 123 I is ideal for a gamma camera with the energy of 159 keV to the patient with a much less radiation dose whereas the radionuclide 124 I is a positron emitter and is useful in some positron emission tomography (PET) for radiopharmaceuticals. The gamma ray will penetrate tissue very effectively without an excessive radiation dose. Iodine-123 decays by electron capture emitting gamma rays at 0.028 and 0.160 MeV that has high penetration power to tissue but no excessive radiation dose. The half-life of 4.2 d and the 23% positron decay allow localization with monoclonal antibodies, and the PET imaging which makes Iodine-124 radionuclide a good candidate for being a diagnostic and a therapeutic.This study aims on the calculation of the excitation functions for 123 I and 124 I various production mechanisms. TALYS 1.6 is used to calculate the reaction cross sections for 123,124,125 Te bombarded with protons and deuteriums to produce 123,124 I radioisotopes commonly used in medical applications. The calculated results were compared with available experimental results from EXFOR. The results are interpreted in terms of deciding which radoisotope is more appropriate to produce with which reaction and evaluating the effects in the reaction mechanisms. In addition, the relative reaction cross-sections of 123,124 I radioisotopes obtained by bombarding 124 Te target with protons were discussed, and the common reaction for the production of 123 I was evaluated to be the 124 Te(p, 2n) 123 I reaction on the highly enriched 124 Te. Thus, it is considered that a very high level of enrichment on the target must be achieved in order to prevent contamination caused by competing reactions of (p, n) and (p,2n). It is concluded that 123 I production is more suitable for small and mediumi-sized cyclotrons.