Abstract A phenomenological electron gas theory is outlined in which the axially symmetric lattice dynamics model (A–S model) is established as a special form of a more general lattice dynamics model which results in the case of a spherical fermi surface. A generalization of the A–S model to include anisotropic effects is discussed in relation to hexagonal and tetragonal metals. Employing the elastic constants as constraints, we fit the experimental dispersion curves for Mg with considerable success using a third neighbor A–S model. Some general features of the dispersion curves for hexagonal metals are developed entirely in terms of the elastic constants C33 and C44 and compared with existing experimental data.