The elastic constants of single crystals of the cubic Laves phases ZrCo2and HfCo2were determined by the pulse‐echo technique over the temperature range 4.2°–300°K. Debye temperatures for the two materials were computed from extrapolations of the elastic constants to 0°K. The ratio of these Debye temperatures is such as to indicate that the primary difference between the two materials is a difference in vibrational amplitudes resulting from the mass difference between zirconium and hafnium. Further substantiation of a close similarity of interatomic force interactions in the two materials is obtained by comparison of appropriate combinations of lattice parameters and force constants.