The dynamic indentation response of stainless steel sandwich panels with a corrugated core or a Y-frame core has been explored using the finite element method to gain insight into the potential of the cores to mitigate against collisions over a wide range of impact velocities pertinent to land and sea-borne vehicles. Back-supported sandwich panels were impacted on the front face by a flat-bottomed or a circular punch at constant velocity ranging from quasi-static loading to 100 m/s. At velocities below 10 m/s the forces on the front and back faces are equal but inertia stabilisation raises the peak load above its quasi-static value. This strength elevation is greater for the corrugated core than for the Y-frame core, and more pronounced for the flat-bottomed punch than for the circular punch. For velocities greater than 10 m/s, the indentation force applied to the front face exceeds the force transmitted to the back face due to plastic-shock effects. In this regime, the force transmitted to the back face by the Y-frame core is markedly less than for the corrugated core, and this brings a performance benefit to the Y-frame, i.e. it protects the underlying structure in the event of a collision.