We present in this work a collection of fundamental solutions, or so-called Green's functions, for some classical or canonical problems in elastodynamics. Such formulas provide the dynamic response functions for transient point sources acting within isotropic, elastic media, in both the frequency domain and the time domain, and in both two and three dimensions. The bodies considered are full spaces, half-spaces, and plates of infinite lateral extent, while the sources range from point and line forces to torques, seismic moments, and pressure pulses. By appropriate convolutions, these solutions can be extended to spatially distributed sources and/or sources with an arbitrary variation in time.

These fundamental solutions, as their name implies, constitute invaluable tools for a large class of numerical solution techniques for wave propagation problems in elasticity, soil dynamics, earthquake engineering, or geophysics. Examples are the Boundary Integral (or element) Method (BIM), which is often used to obtain the solution to wave propagation problems in finite bodies of irregular shape, even while working with the Green's functions for a full space.

The solutions included herein are found scattered throughout the literature, and no single book was found to deal with them all in one place. In addition, each author, paper, or book uses sign conventions and symbols that differ from one another, or they include only partial results, say only the solution in the frequency domain or for some particular value of Poisson's ratio. Sometimes, published results are also displayed in unconventional manners, for example, taking forces to be positive down, but displacements up, or scaling the displays in unusual ways or using too small a scale, and so forth.