  In the present work, the elastic constants and derived properties of
tetragonal and cubic Heusler compounds were calculated using the high accuracy
of the full-potential linearized augmented plane wave (FPLAPW). To find the
criteria required for an accurate calculation, the consequences of increasing
the numbers of $k$-points and plane waves on the convergence of the calculated
elastic constants were explored. Once accurate elastic constants were
calculated, elastic anisotropies, sound velocities, Debye temperatures,
malleability, and other measurable physical properties were determined for the
studied systems. The elastic properties suggested metallic bonding with
intermediate malleability, between brittle and ductile, for the studied Heusler
compounds. To address the effect of off-stoichiometry on the mechanical
properties, the virtual crystal approximation (VCA) was used to calculate the
elastic constants. The results indicated that an extreme correlation exists
between the anisotropy ratio and the stoichiometry of the Heusler compounds,
especially in the case of Ni$_{2}$MnGa.
