The low-lying phonon dispersion curves of a D0 3 ordered Cu 3 Al͑ϩBe͒ shape-memory alloy were measured, at room temperature, along the ͓ 00͔, ͓ 0͔, ͓ ͔, ͓ 1͔, and ͓ 1 2 , 1 2 , ͔ symmetry directions. As in other bcc metals and alloys, we find that the frequencies of the TA 2 ͓ 0͔ modes are relatively low and that the L͓ ͔ branch exhibits a pronounced dip at ϭ 2 3 . The measured low-lying phonon dispersion curves are quite similar to those of a bcc structure. Actually, a fifth-nearest-neighbor force constant bcc model provides a satisfactory fit to the low-lying phonon dispersion curves of this alloy. This model was used to evaluate the elastic constants, the phonon density of states, and the lattice specific heat. The results of these calculations are in good agreement with macroscopic measurements of the elastic constants and specific heat of this alloy.