Room temperature investigations of the single-crystal elastic moduli and anisotropy of the $epsilon$ phase of iron are performed up to 30.3 GPa using the radial X-ray diffraction technique. The accuracy of the calculated elastic moduli has improved compared to previous measurements using similar techniques because of an increase in accuracy of the measurement, confinement of the sample to limit the effect of plasticity, and better calibration of the stress conditions. The aggregate shear modulus that we obtain is in good agreement with a variety of other experimental deductions but differs from first-principles calculations. The effects of the calibration of stress and micromechanical model on the deduction of elastic moduli and elastic anisotropy are discussed in detail. The anisotropy we obtain has the same order of magnitude as first-principles calculations but the direction is reversed, with a weaker amplitude that previous measurements.