The elastic properties of rocks are influenced by several microstructural variables, including the lattice preferred orientation and grain shape fabric of the mineral phases, variations in the spatial distribution of the mineral phases, the properties of the grain boundaries, and the presence of porosity/fractures. Consequently, in principle, directional variations in these variables can be inferred from seismic velocity anisotropy observations. Experimental seismic velocity measurements made on rocks of well-characterized microstructure may be used to improve the quality of such interferences. However, since most rocks are microstructurally complex, in order to interpret the measurements fully, theoretical analyses which can accommodate all the relevant microstructural variables are required. Theoretical analyses of the requisite sophistication have only recently been developed. We have tested one of these (due to Ponte Casta¿eda and Willis) by using it to calculate the elastic properties of an upper mantle harzburgite and by then comparing the results with experimental velocity measurements to determine if the values of those microstructural variables which are difficult to quantify (grain boundary properties, fracture shape) are physically realistic. We find that they are and conclude that the Ponte Casta¿eda and Willis analysis provides a powerful method for a more detailed assessment of the causes of elastic property anistropy in rocks than has previously been possible.