Several mathematical models have been proposed for calculating fuel rod responses in axial flows based on a single rod consideration. The spacing between fuel rods in liquid metal fast breeder reactors is small; hence fuel rods will interact with one another due to fluid coupling. The objective of this paper is to study the coupled vibration of fuel bundles. To account for the fluid coupling, a computer code, AMASS, is developed to calculate added mass coefficients for a group of circular cylinders based on the potential flow theory. The equations of motion for rod bundles are then derived including hydrodynamic forces, drag forces, fluid pressure, gravity effect, axial tension, and damping. Based on the equations, a method of analysis is presented to study the free and forced vibrations of rod bundles. Finally, the method is applied to a typical LMFBR fuel bundle consisting of seven rods.