  The elastic properties of $Cu-Al-Mn$ alloys with compositions along the
$Cu_3Al \to Cu_2AlMn$ line and $bcc$-based structures, are studied by means of
first-principles calculations. From the calculated elastic constants, the
Zener's anisotropy, sound velocities and Debye temperature are determined. The
theoretical results compare well with the available experimental data. The
influence of vibrations is introduced through the quasi-harmonic Debye model,
and different properties are studied as functions of temperature and
composition.
