  The purpose of this paper is to investigate the fundamental problem of the
non-uniform subsonic motion of a point force and line forces in an unbounded,
homogeneous, isotropic medium in analogy to the electromagnetic
Li\'enard-Wiechert potentials. The exact closed-form solutions of the
displacement and elastic fields produced by the point force and line forces are
calculated. The displacement fields can be identified with the elastodynamic
Li\'enard-Wiechert tensor potentials. For a non-uniformly moving point force,
we decompose the elastic fields into a radiation part and a non-radiation part.
We show that the solution of a non-uniformly moving point force is the
generalization of the Stokes solution towards the non-uniform motion. For line
forces the mathematical solutions are given in the form of time-integrals and,
therefore, their motion depends on the history.
