Earth's inner core exhibits elastic anisotropy, but the cause of the texturing is uncertain: solidification, deformation, or some combination. In experiments presented here we deformed in torsion directionally solidified Zn‐3 wt pct Sn alloys at 0.97 of the melting temperature of pure Zn. We used a Zn‐rich alloy because Zn is hexagonal close‐packed at atmospheric pressure, as is likely Fe under inner core conditions. The directionally solidified alloys have the textured, columnar dendritic microstructure that has been proposed for the inner core. As a control we deformed in torsion the same alloy at the same temperature, but with a starting microstructure that is comparatively fine‐grained, equiaxed, and untextured. We find evidence that the directionally solidified alloys deform by means of grain boundary sliding, presumably accompanied by diffusion near the ends of the columnar crystals in order to preserve macroscopic shape. We also find that the directionally solidified alloys require approximately 3 times the torque to deform to the same strain than do the untextured alloys. Grain boundary sliding and greater hardness are due to insufficient slip systems to accommodate the strain, as a result of the texturing. This is supported by microcracking in the deformed directionally solidified alloys. Although the inner core is unlikely to exhibit semibrittle deformation, the experiments suggest that a directionally solidified inner core could have a higher viscosity than one with a finer‐grained, untextured microstructure and that grain boundary sliding may be a dominant deformation mechanism, in spite of the large grain size.