This work explores the strain dependence of the piezoelectric effect in GaAs and InAs zinc blende crystals. We write the polarization in terms of the internal anion-cation displacement and the ionic and dipole charges. We then use ab initio density functional theory to evaluate the dependence of all quantities on the strain tensor. We investigate which aspects of the elastic and dielectric response of zinc blende crystals are sources of non-linearities in the piezoelectric effect. We observe that the main source of non-linearities is the response to elastic deformation and, in particular, the internal sublattice displacement of the interpenetrating cation and anion sublattices. We show that the internal sublattice displacement dependence on the diagonal stress components is neither symmetric nor antisymmetric in the strain. Therefore, non-linear coefficients of order higher than quadratic are needed to correctly describe non-linear effects. Using a fitting procedure of the ab initio data, we also determine all non-linear piezoelectric coefficients up to the third power in the diagonal components of the strain tensor. We can report that non-linear effects up to third order can be significant in precisely determining the magnitude of the piezoelectric polarization if compressive or tensile strains larger than 10% are present. We notice however that, in nanostructures such as quantum dots, the optical properties are less sensitive to the third order non-linear piezoelectric effect and that third order coefficients can therefore be neglected. © 2013 AIP Publishing LLC.