Recent developments in acoustic and electromagnetic diffraction theory show that the formulation of diffraction problems in terms of integral equations is a subject of growing importance (see Bouwkamp A3)). Therefore, it seems worth while to attempt a generalization of the relevant methods to the field of elasto-dynamic diffraction theory. Now it is a well-known fact that in a homogeneous, isotropic, elastic solid there are two velocities of propagation; the larger of the two is associated with the wave fronts of irrotational or compressional waves, the smaller of the two is associated with the wave fronts of equivoluminal or shear waves. In a medium of infinite extent the two types of waves can propagate independently; however, as soon as boundaries occur, an interaction between the two types of waves takes place. Therefore, the phenomena related to the diffraction of elastic waves are expected to be of a complicated nature.