Abstract: The application of BEM to the calculation of acoustic radiation from closed surfaces in an infinite acoustic medium has the advantages of less memory space, higher accuracy and faster calculating speed. However, the singular integrals and the nonuniqueness problem of surface Helmholtz equation at characteristic frequencies should be dealt with. We suggest in this paper combination of the interior Helmholtz equation and its derivatives with respect to the coordinates of an interior point to form an extra equation, in order to solve the problems of acoustic radiation at various frequencies with surface Helmholtz equation; on the area which includes singular point, singular integrals are converted to ordinary ones by polar coordinate transformation. As an example, the acoustic radiation field of closed axisymmetric surfaces with prescribed surface velocity distribution is calculated in the paper.