The compressibility of the nanolaminated ${M}_{2}\mathrm{Al}\mathrm{C}$ phases (space group $P{6}_{3}∕mmc$) with $M=\mathrm{Ti},\mathrm{Zr},\mathrm{Hf}$ [valence electron concentration (VEC) of the $M$ element of 4], V, Nb, Ta $(\mathrm{VEC}=5)$, and Cr, Mo, W $(\mathrm{VEC}=6)$ is systematically studied in the pressure range from $0\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}\ensuremath{\sim}70\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ using ab initio calculations. These phases are characterized by interleaving of MC and Al layers. For $\mathrm{VEC}=4$, we observe a larger compressibility along the $c$ axis as compared to the $a$ axis. As the VEC is increased to 5, the compressibility in the $c$ direction decreases and becomes comparable to the compressibility in the $a$ direction, whereas at $\mathrm{VEC}=6$, the compressibility in the $a$ direction is larger than that along the $c$ direction. These results are consistent with recent experimental work. Based on a systematic study of the VEC-induced changes in bond stiffness, bond angle, and bond energy, we conclude that the geometric alteration of the bonding configuration in combination with the increase in $M--\mathrm{C}$ bond stiffness is mainly responsible for the observed compressibility change.