A new method of numerical computation of elastic wavefields in regions
containing caustics is tested. The method is an extension of the asym
ptotic ray theory (ART). The essential features of the method consist
of the application of expressions which are well defined at caustics a
nd expressed in terms of ray tracing combined with complex ray tracing
in caustic shadows. The method and an outline of the underlying theor
y are briefly presented, followed by a comparison with finite differen
ces on a test model involving a caustic cusp. The comparison reveals t
he unexpectedly high degree of accuracy of the new method.