The elastic properties of compressed Fe and FeO are examined using density of states measured by nuclear resonant inelastic X-ray scattering. We analyze the data both from non-hydrostatic and nearly hydrostatic experiments. The effects of preferred orientation in non-hydrostatic experiments could be substantial. We present also evidence in favor of strong softening of the Debye sound velocity due to the magnetoelastic coupling in iron oxide near the Nèel transition. The geophysical implications resulting from the elastic and magnetoelastic properties of these and related materials under compression are discussed.