It is generally difficult to calculate the wave excitation forces for three dimensional bodies, so strip method is usually applied to the bodies that have sufficiently long parallel parts, but it can't be applied to axi-symmetrical bodies, circular docks with or without footing, for instance. In this paper, authors deal with the wave excitation forces upon axi-symmetrical bodies by means of the variational method making use of source singularities along symmetrical axis, and give good approximate solutions. At this time, we calculated added masses and damping coefficients for heaving spheroids, circular docks and circular docks with sperical footing by means of the variational method, and then we derived wave excitation forces and amplitude ratio of radiation waves from damping coefficient by the aid of Haskind-Newman's relation, and from these results we showed that three dimensional wave-excitationless forms existed and that they had the same character as two dimensional wave-excitationless forms. The variational method employed here has been developed by Professor M. Bessho. The results show the good agreement with model experiments, and calculations of Havelock and W. D. Kim.