The paper reviews the theoretical basis and the historical background of the Fourier-Bessel representation of the solution to seismic problems in layered media. The paper shows how to incorporate point sources into the process based on integrating an ordinary differential system. The final form of the solution is given for the following cases: (1) an explosive source acting inside a liquid, solid, or mixed structure, (2) an internal torque pulse, and (3) a concentrated force acting on the surface. The paper ends with an example showing that ''upgoing'' and ''downgoing'' waves are present in an inhomogeneous structure, even when the integration of the differential system is performed in only one direction. ¿ American Geophysical Union 1992