Values of release wave speed in shock-compressed polycrystalline alumina and aluminum (2024) have been measured to 400 and 260 kbar, respectively. These values, as well as previous data for aluminum and iron, have been compared with fourth-order finite strain extrapolations of the longitudinal sound speed Vp. For alumina in the pressure range 200--300 kbar and for α iron and &egr; iron the observed release wave speeds fall below any reasonable extrapolation of Vp. In the range 360--400 kbar the data for alumina indicate that M (∂2M/∂P2) ?-50 (where M and P are longitudinal modulus and pressure, respectively); this value is in approximate agreement with Graham's ~200-kbar data on elastic shock compression of single-crystal aluminum oxide. For aluminum the data indicate a value for M (∂2M/∂P2) of 2.7¿5.7.