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Mechanical joints such as bolted and spot welded joints are widely used to join plate structures. The existence of contact interface in the joint increases the vibration damping in the structure because the energy dissipation due to friction occurs at the interface. In this paper, we propose a procedure for calculating the energy dissipation at the interface using finite element analysis to estimate the damping for the fundamental and the higher modes. We use the static contact analysis instead of the dynamic contact analysis to reduce computational effort and use the mode shapes of linear FE model of the joined plate structure as the forced displacement in the static contact analysis. This enables us to obtain the energy dissipation depending on the mode shape for each mode. To improve the calculation accuracy of the energy dissipation, we apply a surface load on the overlap (interface) region and find the necessary value of surface load. To validate the proposed procedure, the modal damping ratios estimated from the dissipated energy are compared with the measured damping ratios. The results show that the proposed procedure enables to accurately estimate the energy dissipation of the joined plate structure. The necessary surface load increases with increasing mode number and varies almost proportionally with the square of the angular frequency.