The sodium-cold pool-type fast reactor is the preferred reactor type for the fourth generation advanced reactor research. The reactor structure of a pool-type fast reactor has the characteristics of large size, thin wall, and relatively low stiffness. Therefore, the seismic design, analysis, and verification of the pool-type fast reactor are the key concerns of the fast reactor safety evaluation. In the fast reactor, many important reactor structures, such as the main pump support cylinder, are immersed in the ring basin of the reactor body. These devices are equipped with thermal shields and can therefore be regarded as coaxial housing systems with water gaps between the cylinders. Under the seismic condition, the fluid-structure coupling effect between the shell and the water gap will change the natural frequency of the shell itself, and the change of structural vibration characteristics is very important to study the seismic performance of the equipment structure in the fast reactor. However, the calculation method based on the dry/wet modal frequency ratio is not suitable for the calculation of additional mass under non-full water conditions. In this paper, based on ANSYS finite element analysis method, a coaxial three-layer shell model with fluid clearance is established to simulate the main pump supporting cylinder and other equipment, and the modes under different frequencies are studied. The additional mass of fluid clearance under different modes is calculated by the relationship between fluid pressure field and shell areal-displacement during vibration. The results are of reference value to the structural design and test of coaxial multi-layer shells such as the support cylinder of the main pump of the fast reactor.