  This paper is concerned with the problem of scattering of a time-harmonic
electromagnetic field by a three-dimensional elastic body. General transmission
conditions are considered to model the interaction between the electromagnetic
field and the elastic body on the interface by assuming Voigt's model. The
existence of a unique solution of the interaction problem is proved in an
appropriate Sobolev space by employing a variational method together with the
classical Fredholm alternative. The inverse problem is then considered, which
is to recover the elastic body by the scattered wave-field. It is shown that
the shape and location of the elastic body can be uniquely determined by the
fixed energy magnetic (or electric) far-field measurements corresponding to
incident plane waves with all polarizations.
