The inner core of the earth most likely consists of &egr; (hcp) iron and shows anisotropy of seismic velocities which could be explained by crystallographic preferred orientation developing during convective flow. This paper summarizes deformation mechanisms in hcp metals and applies the Taylor theory of polycrystal deformation to analogs of &egr;-iron for different strain histories. The pattern of preferred orientation is then used to calculate elastic properties of deformed polycrystals with special emphasis on anisotropy. ¿ American Geophysical Union 1988