There is a strong correlation between the measured elastic anisotropy of dunite and the preferred orientation of its main component, olivine. Olivine is a major constituent of the mantle and dunite is considered representative of upper mantle materials. In this report the measured elastic wave velocities for a dunite from Hidaka Horoman are used to determine the coefficients W1mn of a series expansion of the crystallite orientation distribution function in generalised Legendre functions. This function gives the probability of a crystallite having a given orientation with respect to a set of axes fixed in the rock. The solution to this problem allows construction of crystallographic pole figures, which indicate a strong alignment of olivine a-axes in agreement with the conclusions of petrofabric examination. Seismic studies of the crystallite orientation distribution function are therefore feasible and these should lead to a better understanding of the deformation processes associated with flow in the upper mantle. ¿ American Geophysical Union 1987