The contributions to the elastic shear constants of beryllium at 0°K were calculated on the basis of an energy band model for this metal proposed by Herring and Hill. The results are compared with those obtained assuming nearly‐free‐electron and free‐electron behavior for the valence electrons. It was found that the valence electron contribution was very sensitive to the shape of the energy bands and hence the Fermi contribution to the elastic shear constants was strongly dependent upon the energy band model chosen. On the basis of the model proposed by Herring and Hill the elastic shear constants of beryllium, like the alkali metals, are predominantly determined by the electrostatic energy of the ion‐cores.