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The free-surface Green function method is widely used in solving the radiation or diffraction problems caused by a ship or ocean structure oscillating on the waves.In the context of inviscid potential flow,hydrodynamic problems such as multi-body interaction and tank side wall effect cannot be properly dealt with based on the traditional free-surface frequency domain Green function method,in which the water viscosity is omitted and the energy dissipation effect is absent.In this paper,an open-sea Green function with viscous dissipation was presented within the theory of visco-potential flow.Then the tank Green function with a partial reflection from the side walls in wave tanks was formulated as a formal sum of open-sea Green functions representing the infinite images between two parallel side walls of the source in the tank.The new far-field characteristics of the tank Green function is vitally important for improving the validity of side-wall effects evaluation,which can be used in supervising the tank model tests.