The paper deals with the treatment of artificial boundaries within the
framework of characteristic-based finite difference methods for the p
ropagation of elastic waves inlarge or infinite solids. In order to re
strict the computational domain mainly to the area of technical intere
st and to suppress non-physical reflections on its boundary, an absorb
ing transition layer adjacent to this kernel area is used. The transit
ion layer is designed to match the material properties in the kernel a
rea so that outgoing waves can propagate across the interface between
the kernel area and the transition layer without reflection and are al
most absorbed in that layer. Two different techniques are adopted for
the transition layer. One gradually reduces the amplitude of waves in
the transition layer, and the other modifies the wave speeds there. To
gether with dissipative finite difference schemes, both techniques sho
w numerical efficiency. Numerical examples including cracked media, wh
ere plane wave fronts: and curved wave fronts (e.g. radiating from the
crack tip) occur, are presented.