  The equations of motion governing small elastic oscillations of materials,
induced by gravitational waves, are derived from the general framework of
Carter and Quintana. In transverse-traceless gauge, no bulk forces are present,
and the gravitational wave is found to act as an effective surface traction.
For thin rods, an equivalent description is given, in which there is no surface
traction, but a bulk acceleration, which is related to the Riemann curvature of
the gravitational wave. The resulting equations are compared to those of the
Synge-Bennoun elasticity theory.
