A very simple technique for the computation of two-and three-dimensional potential flows, based on the method of singularities, has been initiated by A. M. O. Smith and his collaborators and developed by them into a successful standard procedure at Douglas. The program assumes a representation of the immersed body by straight respectively planar facets or elements on each of which a constant source distribution is taken to act. The associated velocity field is easily established and the intensity of the sources determined from the boundary condition of zero normal velocity in the compound flow. It appears reasonable to expect a higher degree of accuracy by the adoption of a more sophisticated source distribution and the use of curved surface elements which allow a better approximation to the actual geometry. Experience in structural analysis has clearly shown that the gain in accuracy achieved by more elaborate elements increases at a higher rate than the corresponding programming effort.