Structural, thermoelastic, and mechanical properties of ZnO, ZnS, ZnSe in wurtzite and zinc blende phase have been studied using SIESTA code. The elastic anisotropies in the single crystal were analysed by means of the directional dependence of Young, shear, and bulk moduli, and Poisson ratio. Using the Voig-Reuss-Hill approximation, we obtained the bulk and shear moduli, two essential properties in the polycrystalline characterization. In addition, our ab-initio results such as PAO's radii, Mulliken population and lattice properties were introduced in the Šimůnek et al. model giving Vickers hardness values in good agreement with experimental range. To our knowledge, the hardness in ZnO(zinc blende) and ZnSe(wurtzite) had been estimated for the first time. A better structural stability and resistance in ZnO/ZnS than ZnO/ZnSe alloys in the wurtzite phase is found. The volumetric thermal expansion coefficient was calculated in the stable natural phases using the Grüneisen parameter and the heat capacity, at 300 K. Our results predict an improved thermal stability in the ZnO/ZnS heterojunctions as compared to ZnO/ZnSe. •SIESTA together with Šimůnek et al. model allow us to predict hardness in ZnO, ZnS and ZnSe.•ZnO(zincblende) will show a resistance to deformation larger than ZnSe(wurtzite).•ZnO/ZnS alloys could be more resistance to a plastic deformation than ZnO/ZnSe alloys.•Expansion coefficients could justify the thermal stability of ZnO/ZnS heterojunctions.