A new method is given for computing effective polycrystalline elastic constants from single‐crystal elastic coefficients. Agreement with observation is good. The method is based on the assumed equivalence of the lattice‐vibrational properties of single crystals and polycrystals of the same material; single‐crystal and polycrystal Debye temperatures are equated. Present predictions of polycrystal elastic moduli differ significantly from those of most other averaging methods by being lower than the familiar Voigt‐Reuss‐Hill results.