Elastic behavior under pressure of the vacancy compounds ${\mathrm{Hg}}_5$${\mathrm{Ga}}_2$□${\mathrm{Te}}_8$, ${\mathrm{Hg}}_3$${\mathrm{In}}_2$□${\mathrm{Te}}_6$, and Hg${\mathrm{In}}_2$□${\mathrm{Te}}_4$

${\mathrm{Hg}}_5$ ${\mathrm{Ga}}_2$□${\mathrm{Te}}_8$, ${\mathrm{Hg}}_3$ ${\mathrm{In}}_2$□${\mathrm{Te}}_6$, and Hg${\mathrm{In}}_2$□${\mathrm{Te}}_4$ are semiconducting vacancy compounds which may be thought of as having tetrahedrally coordinated structures with a sublattice of unfilled sites. Measurements of the hydrostatic pressure dependences of ultrasonic-wave transit times in single crystals of these compounds have been made and used to obtain the pressure derivatives of the elastic-stiffness constants. The elastic behavior of these compounds under pressure is compared with that of the "parent" zinc-blende-structure compound HgTe. It is found that the compression $\frac{V\left(P\right)\mathrm{}}{V_0}$ of the vacancy compounds becomes larger as the proportion of empty cation sites is increased. The effect of hydrostatic pressure on the gradient of the acoustic-phonon branches at the Brillouin-zone center is discussed in terms of the mode-Grüneisen gammas. The presence of the sited vacancies is shown to inhibit the softening of shear modes characteristic of HgTe and related zinc-blende-structure compounds. Thus, for vacancy compounds, the shear-to-bulk modulus ratios $\frac{1}{2}\frac{(C_{11}-C_{12})}{B}$ and $\frac{C_{44}}{B}$, or the ratio $\frac{\beta }{\alpha }$ of the bond-bending to -stretching force constants, do not reach the limiting values for crystal stability and the densification transition until much higher pressures than that found for HgTe.