This paper presents a computational technique using Boundary Element method for the prediction of sound radiated by axisymmetric bodies with arbitrary boundary conditions. By taking the advantage of the axisymmetric property of the body the three dimensional integral formulation is reduced to one dimensional integral along the generator of the body. The arbitrary boundary conditions is expanded in Fourier series with a period of 2π. The integral equation is solved using superposition principle involving each term of the series. By adding the result associated with each term the final solution is obtained. A numerical procedure is implemented using curvilinear isoparametric element representatation. Examples are given involving an oscillating sphere and a half vibrating sphere. The results are compared with the analytical solution in which good agreement has been obtained.