Fluid damping acting on structures in confined fluid can significantly affect the seismic responses of the structures. This paper presents an analytical and experimental study for evaluating fluid damping of vibrating rectangular rods in a cylindrical vessel which is filled with liquid. In the analysis, the fluid inertia force, that is, added mass, and the flow velocity on the rods are approximately obtained under the assumption of the potential flow. The drag force, that is, the damping force, is assumed to be proportional to the drag coefficient Cd and the flow velocity squared. In the experiment, vibration tests using physical models of the rectangular rods were performed. The measured fluid damping data of the rods are compared with the analytical values to examine the validity of the analytical method.