In wave physics, the geometrical limit is defined as a propagation regime where the scattering cross‐section of an object becomes independent of its internal structure and tends to twice its geometrical cross section as the frequency goes to infinity. This is a result that is particularly well documented in the field of optics. Following the classification of Wu and Aki (1985b), we study the high‐frequency scattering limit for velocity‐type and impedance‐type elastic perturbations. Although velocity‐type scatterers do follow the geometrical limit of , the scattering cross section of any impedance‐type scatterer depends on both its density and elastic properties at all frequencies. These results are illustrated using the example of a spherical inclusion that exhibits a small contrast of properties with its environment. We derive simple asymptotic formulas that show good agreement with exact solutions of the boundary value problem (BVP). Our results confirm the distinct behavior of velocity‐type versus impedance‐type perturbations at all frequencies.