Accurate modeling of meteorite impacts, and deformation of planetary cores require characterization of the flow strength and in-elasticity of iron in its different phases. In this Letter, we investigate the flow strength of both the ambient α phase and high-pressure ε phase of iron at strain rates of 1×10^{5} s^{-1} and pressures up to 42 GPa using high-pressure-pressure shear plate impact experiments. We report the strength of the ε iron to be significantly higher than α phase but consequently one order smaller than the previously reported dynamic strength at high pressures. The complete stress-strain response of the ε phase is reported for the first time.