In this study, we conducted a comparative study on the neutron and gamma photon shielding performance of three shielding materials, boron carbide (BC), stainless steel (SS), zirconium hydride (ZrH) and some of their mixture. Reducing the thickness of the shielding layer is also one of the objectives of the study. In addition to shielding characteristics, the impact of various shielding materials on the reactor’s physical parameters has also been studied, such as the neutron energy spectrum, the distribution of neutron flux in the whole core and on the outer surface of the shielding layer, neutron and gamma photon dose rates etc. It has been found that the neutron leakage can be effectively reduced when using ZrH as a shielding layer. However, the number of thermal neutrons on the inside of the core cannot be absorbed effectively. Therefore, a method has been proposed to add BC, which has a large thermal neutron absorption cross-section, to the ZrH material. The results indicate that the use of ZrH-BC mixed material (BC content is 10%) as a side shield for small annular fuel sodium-cooled fast reactors can not only compensate for the defects of ZrH as a shielding layer but also effectively reduce the thickness of the shielding layer. Compared to using 100% BC material as a shielding layer, the thickness can be reduced by approximately 15.54%. It has been proven that ZrH-BC mixed material possesses excellent shielding properties against both neutrons and gamma photons. Additionally, it demonstrates a promising application potential in the shield design within the field of nuclear engineering.