The anisotropy and phonon focusing of AlLi are investigated 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 results are explained in terms of phonon focusing due to the fact that in elastically anisotropic crystals. The propagation of elastic waves in AlLi is affected by the elastic anisotropy of the lattice. (C) 2014 Elsevier B.V. All rights reserved.