The elastic anisotropy of rocks is due to the petrofabric structure of anisotropic minerals and/or to the configuration of interface between the constituent mineral grains. With respect to the dilatational wave, the degree of anisotropy of dunite is estimated as follows : 2.5 per cent utmost due to interface configuration and 10 per cent ordinarily due to petrofabric structure of olivine. The origin of the preferred orientation of olivine in massive ultrabasic rocks is discussed based on the nonhydrostatic thermodynamic theory. It is inferred that the olivine crystals in the upper mantle will show a remarkable preferred orientation especially in the tectonically active region where the nonhydrostatic condition prevails. If the peridotite is the main constituent of the upper mantle, its significant anisotropy (about 5 per cent) will be detectable from the analysis of seismic wave propagation. On the other hand eclogitic rocks are considered to be comparatively isotropic. Therefore, it might be possible to determine by seismic prospecting whether the upper mantle is peridotitic or eclogitic.