The anisotropic mechanical response of ZIF-8 and ZIF-67 is investigated as a function of pressure and its main features (including shear-destabilization eventually leading to amorphization) discussed in terms of specific lattice vibrations and structural changes occurring in the framework. At zero pressure, the two ZIFs are characterized by an elastic anisotropy with directions of maximum and minimum stiffness along ⟨111⟩ and ⟨100⟩, respectively. At P=0.2 GPa, the framework exhibits a perfectly isotropic mechanical response, while at P>0.2 GPa a different (complementary) anisotropic response is observed with directions of maximum and minimum stiffness along ⟨100⟩ and ⟨111⟩, respectively. The bulk modulus of the two ZIFs initially slightly increases up to 0.1 GPa of pressure and then decreases at higher pressures. Amorphization in both ZIF-8 and ZIF-67 is confirmed to be due to the pressure-driven mechanical instability of their frameworks to shear deformations. The directional elastic moduli of the two ZIFs are partitioned into contributions from specific normal modes of vibration. The elastic constants C11, and C12 [and thus the bulk modulus K=1/3(C11+2C12)] are mostly affected by symmetric “gate-opening” vibrations of the imidazolate linkers in the four-membered rings. The C44 shear elastic constant (and thus the mechanical instability and amorphization of the framework) are instead related to asymmetric “gate-opening” vibrations of the four-membered rings.