Reformulation of the elastodynamics problem as a system of first‐order partial differential equations is reviewed and preliminary results are presented for isotropic and anisotropic materials that suggest that the approach will extend in a reasonable way to analysis of more general materials. The propagating fields are expressed as a sum of characteristic propagation modes of an expanded acoustic matrix, which include the stress terms as well as the displacements. Boundary projection operators for the reflection and refraction coefficients are determined and the classic Frennel coefficients are recovered as particular examples within a general theory. © 2003 American Institute of Physics