In a homogeneous, isotropic, perfectly elastic medium a scattering obstacle of finite extent is present. When a plane, time‐harmonic, elastic compressional (P) or shear (S) wave is incident on it, the extinction cross section (i.e., the sum of the scattering and the absorption cross section) of the obstacle is directly related to the far‐zone amplitude of the particle displacement of the scattered wave, observed exactly behind the obstacle. This relationship is discussed. In spite of the fact that in elastodynamic scattering the scatteredPwave as well as the scatteredswave contribute to the time‐averaged scattered power, the extinction cross section appears to depend only on the value of that farfield scattered‐wave amplitude which is of the same type (PorS) as the incident wave.Subject Classification: [43]20.15, [43]20.30.