The sound radiation of oscillating structures of arbitrary shape into three-dimensional space will be calculated by representing the normal velocity on the surface as a superposition of multipoles. Depending on the geometry of the radiator, one or more source locations in the interior volume are selected. Different variants of this technique (null field method, weighted residual methods, etc.) and their interdependence will be discussed. The advantage of the method is a strongly reduced calculation time for complex structures. A disadvantage is the presently still incomplete investigation of the convergence behavior. For this reason a boundery element method will alternatively be applied to the discretized Kirchhoff-Helmholtz integral equation, which will be solved on grids of varying size (multigrid method). Both methods will be used to calculate the radiation from spheres, cylinders, cubes, etc. Results will be compared to analytical solutions, numerical results obtained by other techniques, and experimental data. [Work supported by the Department of Research and Technology of the Federal Republic of Germany (BMFT).]