Elastic radiative transfer equations have recently been derived to describe the evolution of seismic energy in the crust of the earth (Ryzhik et al., 1996). These equations are derived from a rigorous statistical treatment of the elastic-wave equation and include both shear polarizations and mode conversion between the P and S modes. Calculations of attenuations ratios and diffusion constants based upon these theories are made and compared with values used in the literature. Equivalent elastic radiative transfer equations have also been previously derived for ultrasonic materials characterization purposes using a different method. Observations made from numerical solutions of these ultrasonic radiative transfer equations are discussed with application to seismology. Both the steady-state and time-dependent solutions have been examined including effects from boundaries, depolarization of S waves approach to isotropy of energy, and validity of the diffusion approximation. Similar results are expected for seismology.