Recent numerical-modelling and seismological results have raised new questi
ons about the dynamics(1,2) and magnetism(3,4) of the Earth's core. Knowled
ge of the elasticity and texture of iron(5,6) at core pressures is crucial
for understanding the seismological observations, such as the low attenuati
on of seismic waves, the low shear-wave velocity(7,8) and the anisotropy of
compressional-wave velocity(9-11). The density and bulk modulus of hexagon
al-close-packed iron have been previously measured to core pressures by sta
tic(12) and dynamic(13,14) methods. Here we study, using radial X-ray diffr
action(15) and ultrasonic techniques(16), the shear modulus, single-crystal
elasticity tensor, aggregate compressional- and shear-wave velocities, and
orientation dependence of these velocities in iron. The inner core shear-w
ave velocity is lower than the aggregate shear-wave velocity of iron, sugge
sting the presence of low-velocity components or anelastic effects in the c
ore. Observation of a strong lattice strain anisotropy in iron samples indi
cates a large (similar to 24%) compressional-wave anisotropy under the isos
tress assumption, and therefore a perfect alignment of crystals(6) would no
t be needed to explain the seismic observations. Alternatively the strain a
nisotropy may indicate stress variation due to preferred slip systems.