We have studied the structural, elastic, electronic and phonon properties of LiMgP and LiMgAs in the alpha, beta and gamma phases by employing the plane wave pseudopotential method based on density functional theory, within the local density approximation. Lattice parameters, bulk modulus and its pressure derivative, and second order elastic constants were found in good agreement with the literature data. We found that the gamma phase of these compounds are in metallic nature as opposed to alpha and beta phases. A linear-response approach to density functional theory was used to derive the phonon dispersion and the phonon density of states. The calculated zone-center optical phonon modes for these materials were compared with available experimental and theoretical results. Atomic displacement patterns for LiMgP in alpha phase at Gamma and X symmetry points were presented. (C) 2012 Elsevier B. V. All rights reserved.