A simplified finite element has been developed for modeling the added mass and inertial coupling arising when clusters of cylinders vibrate in a quiescent fluid. The element, which is based on two-dimensional potential flow theory, directly couples two adjacent beam elements representing portions of the adjacent cylindrical structures. The primary advantage of this approach over existing methods is that it does not require the discretization of the surrounding fluid and, therefore, is computationally much more efficient. The fundamental frequencies of tube bundles of various pitch ratios have been predicted using this method and compared with experimental data. Generally, the agreement is good, especially for the bandwidth of fluid coupled natural frequencies. The transient response of tube bundles is also examined using time integration of the finite element model. The beating phenomenon and time decay characteristics exhibited by the experimental bundles under single-tube excitation are well predicted and valuable insights are gained into the measurement of damping in tube bundles.