Scattering cross-sections are calculated for a crack in three-dimensional elastic solids. The crack opening displacements are evaluated first by the boundary element methods. Then the scattering amplitudes for the crack are derived from the far-field representations of the scattered fields. In the final step to calculate the scattering cross-sections from scattering amplitudes, two methods are compared. One is the method based on the definition and here the scattering cross-section is calculated from the integration of the differential cross-sections over the solid angle. The other is the method based on the elastodynamic counterpart of the optical theorem. It is verified that the results obtained from the elastodynamic optical theorem are accurate enough to evaluate the scattering cross-section for the crack in elastic solids.