EN
In this paper we present a method of calculating third-order elastic constants C_{ijk} and its application to zinc-blende nitrides AlN, GaN, and InN. Our approach is based on accurate ab initio calculations of both energy and stress as a function of applied strain. Ab initio computations are performed within density functional theory framework. To assess the reliability of the presented method, we compare our theoretical findings for GaAs with experimental results for C_{ijk} available for this material.