Rare event search experiments are one of the most important topics in the field of fundamental physics, and high-purity germanium (HPGe) detectors with an ultra-low radioactive background are frequently used for such experiments. However, cosmogenic activation contami-nates germanium crystals during transport and storage. In this study, we investigated the movable shielding con-tainers of HPGe crystals using Geant4 and CRY Monte Carlo simulations. The production rates of 68Ge, 65Zn, 60Co, 55Fe, and 3H were obtained individually for different types of cosmic rays. The validity of the simulation was confirmed through a comparison with the available exper-imental data. Based on this simulation, we found that the interactions induced by neutrons contribute to approxi-mately 90％ of the production rate of cosmogenic activa-tion. In addition, by adding an optimized shielding structure, the production rates of cosmogenic radionuclides are reduced by about one order of magnitude. Our re-sults show that it is feasible to use a shielding container to reduce the cosmogenic radioactivity produced during the transport and storage of high-purity germanium on the ground.