This transport cask for radioactive materials will be used in the Gijang reactor. It will transport the Ir-192 10,000 Ci or I-131 80 Ci. In this case, the safety evaluation, such as protection of leakage of radioactive material, and radiation shield should be carried out before it is used in the research reactor. The safety regulation requires various tests, such as water spray, free drop, penetration, and water immersion. But this paper considers only the regulations related with thermal-stress and drop impact under the normal conditions because it will be used only in the research reactor building. In this paper, coupled numerical analysis was performed using finite element simulation to investigate the effect of position of tungsten and lead to enhance the safety of transport cask. As a result of simulation, it was verified that the Tungsten-Lead structure is the most durable among the cases considered in the study with a viewpoint of thermal-stress and drop impact.