We have performed a first-principles full-potential augmented-plane wave plus local orbitals (FP-APW+lo) calculations with density functional theory in local density approximation, in aim to determine and predict the pressure dependence of elastic constants of BN, AlN, GaN and InN compounds. From our results, we sustain the idea of no evidence that the soft acoustic mode is responsible for the phase transition. (C) 2004 Elsevier Ltd. All rights reserved.