Seismic evidence suggests that the solid inner core of the Earth may be anisotropic. Several models have been proposed to explain this anisotropy as the result of preferred orientation of crystals. They range from a large annealed single crystal, growth at the melt interface, to deformation-induced texture. In this study texture development by deformation during inner core convection is explored for ϵ-iron (hcp) and &ggr;-iron (fcc). Convection patterns for harmonic degree two were investigated in detail. In the model it is assumed that traces of potassium are uniformly dispersed in the inner core and act as a heat source. Both for fcc and hcp iron, crystal rotations associated with intracrystalline slip during deformation can plausibly explain a 1--3% anisotropy in P waves with faster velocities along the N-S axis and slower ones in the equatorial plane. The effect of single crystal elastic constants is explored. ¿ 2000 American Geophysical Union