Using Buckingham potentials we study zinc spinel ferrites ZnFe2O4 mechanical properties such as elastic constants, bulk moduli and vacancy formation energies EV at zero temperature. These properties are analyzed as a function of the lattice parameter, the pressure and the inversion degree parameter. The potentials predict the geometry of normal and partial inverse spinels in good agreement with reported experimental data. Statistical randomness of the octahedral sites in partial inverse spinels is implemented to investigate its effects in energies, the lattice parameter, the elastic constants and bulk moduli. The results show that deformations of up to ±6% are associated with pressures of up to 50 GPa, and that the normal spinel at zero pressure is in the limit between brittle and ductile, (B/G ​ = 1.77). Besides, positive pressures make the normal spinel brittle while negative ones transform it into ductile. However, the partial inverse spinels are ductile materials whose ductility increases with the inversion degree. It is also found that EV (O) ≤ EV (Zn) ≤ EV (Fe) and that these computations require a large box size. Our results show that fluctuations due to randomness of Ze and Fe play an important role in the formation of vacancies in the inverse spinel and their stability, but they can be safely ignored for elastic constants. The results are compared to experimental data found in the literature.