For the seismic design and analysis of LMR(liquid metal reactor) being developed in Korea, it is necessary to develop the simple seismic analysis model including the fluid-structure interaction effects. In this paper, the theoretical backgrounds for the fluid added mass of the immersed concentric cylinders are investigated and the seismic analysis code using the Runge-Kutta algorithm, which can consider the fluid added mass matrix in system matrix, are developed to perform the time history seismic analysis. Form the coupled modal analysis and the seismic analysis for the simple immersed concentric cylinders, it is verified that the fluid added mass significantly affect the vibration characteristics and the seismic responses. Therefore the fluid coupled effects should be carefully considered in seismic response analysis of the immersed concentric cylinders.