The response of a system, consisting of two elastic half spaces in contact at a plane interface, has been investigated for different types of “line sources.” I use the term “line source” to designate a source of elastic energy which has the following properties: (1) the source has a uniform cross-section along its length, (2) the source axis is a straight line which extends to infinity in both directions, and (3) the components of stress and displacement in the radiated waves are constant at each instant of time along lines which are parallel to the source axis. Consider first the case of a line source having a circular cross-section. The source, itself, is then a cylinder which extends to infinity in both directions. Nothing has been said previously about the condition of stress and displacement on the periphery of the cross-section formed by the intersection of a plane whose normal is parallel to the source axis with the source itself. The assumption which leads to the greatest simplification mathematically is that the functions which specify how the components of stress and displacement vary with time are independent of position on the periphery of the cross-section and that at each instant of time the stress and displacement components are uniform on the periphery of the cross-section. A cylindrical source of this type will be referred to as a compressional source if at each point the displacement is in the radial direction, a torsional source if the displacement is tangent to the cylindrical surface and in a plane whose normal is parallel to the axis, and an SH source if the displacement is tangent to the cylindrical surface and parallel to the axis.