Some axially symmetric singular solutions are derived for an elastic space subjected to the action of time-dependent body forces. These singular solutions may also be defined as the axisymmetric elastodynamic Green's functions. They correspond to the cases where a unit concentrated force (time-harmonic or transient) is uniformly distributed along circular rings, in the axial, radial and tangential directions, respectively. Using these solutions, it is possible to derive new singular solutions corresponding to distributed singularities.