Abstract: In this paper a numerical method for calculating the hydro-dynamic coefficients for vertical plane wave motion problems in deep water is described. This procedure is developed by using the wave source method based on Green’s theorem. The applications of the method to the cases of semi-circular and rectangular section bodies subjected to linear waves are presented, here, and the computed results are compared with the earlier experimental data of Vugts.

Key words: upper triangular infinite-dimensional Hamiltonian operator, eigenvector, root vector, multiplicity, completeness