With the advancement of medical technology in recent years, the use of Gamma Knife equipment for non-invasive and painless lesion treatment has significantly increased. The integrated structure of the cobalt source and the cylindrical drawer is a typical configuration commonly employed in Gamma Knife systems. Therefore, it is essential to design a drawer-type cobalt source transport container that offers reliable performance and ease of operation. In this configuration, the aperture of the drawer extends radially through the cylinder of the container, resulting in radiation streaming at the corresponding sides of the container at both ends of the drawer. Consequently, the work aims to address the radiation streaming phenomenon from a design optimization perspective and analyze the distribution characteristics of the leakage region on the exterior of the container. A series of studies on a drawer-type container with a classical configuration were conducted with the high-precision Monte Carlo computational program to model and analyze its primary radiation screaming path (drawer apertures and aperture gaps between the drawers). According to the analysis results, the size of the aperture gap, the distance between the aperture gap and the radioactive source, and the location of the radioactive source significantly affected the radiation dose level outside the container. The dose rate of the radiation leakage beam increases rapidly with the increasing distance between the aperture gap (up to 10 mm) and the active zone of the radioactive source, relative to the center of the source drawer. Design units can utilize this conclusion to optimize the shielding performance of the container. Furthermore, the maximum impact area of radiation streaming outside the container deviates from the center of the drawer. As the distance from the container increases, this deviation increases. Operators can leverage this characteristic to effectively avoid the path of radiation streaming.