Natural Science Foundation of the Education Department of Henan Province of China [2009B590001]; Henan Science and Technology Agency of China [092102210314, 132102210207]; State Key Laboratory of Superhard Materials (Jilin University) [201107]; National Natural Science Foundation of China [11104127] ; We have investigated the anisotropy and phonon focusing of NiAl using ultrasoft pseudopotentials within the generalized gradient approximation correction in the frame of density functional theory. Theoretical calculation of the three dimensional slowness surfaces gives insights into the mixing of longitudinal and transverse modes and shows the origin of the phonon caustics. The phonon focusing due to the elastically anisotropy, and the phonon phase and group velocities are explained. In general, the propagation of elastic waves in crystals is strongly affected by the elastic anisotropy of the lattice. (C) 2013 The Authors. Published by Elsevier Ltd. All rights reserved.