The development of fast reactor is playing an increasingly important role in the sustainable development of nuclear energy. The sodium-cooled fast reactor has become the preferred reactor type among the six advanced reactors of the fourth generation because of its inherent safety and advantages in proliferation-resistant nuclear fuel. There are many filled liquid narrow gap multi-layer concentric thin-walled structures (such as main pump support cylinder and its thermal shielding) in the sodium-cooled fast reactor. Under seismic conditions, such concentric thin-walled structures are affected by the relatively strong fluid–structure coupling effect, which will change their vibration characteristics and natural frequencies. Therefore, it is of great significance to study the fluid–structure coupling characteristics of concentric cylindrical shells with double layers. At present, there are few studies on the vibration modes and added masses of concentric double-layer cylindrical shells with weights at the top of inner cylinder, such as main pump support cylinder and its thermal shielding. For flexible concentric cylindrical shells, due to the coupling effect between inner and outer shells, there will be vibration modes of inner and outer shells in the same direction and opposite direction. In this paper, finite element models of concentric cylindrical shells with water and without water are established by using ANSYS software. The vibration modes and added masses of concentric cylindrical shells are calculated, and the influence of different fluid gaps on vibration modes is explored.