We have studied structural, elastic, and lattice dynamical properties of the LuB2, LuB4, and LuB12 compounds by using the plane-wave pseudopotential approach to the density-functional theory within the generalized gradient approximation. We have considered three different crystal structures of LuBx: LuB2 (P6/mmm), LuB4 (P4/mbm), and LuB12 (Fm-3m). The most stable structure is found to be tetragonal (P4/mbm) structure. The comparative results on the basic physical parameters such as lattice constants, bulk modulus, bond distances, elastic constants, shear modulus, Young's modulus, and Poison's ratio are reported. Also, we have predicted that LuB4 and LuB12 compounds are potential superhard materials. Furthermore, the phonon dispersion curves and corresponding phonon density of states (DOS) are computed for considered phases. Our structural and some other results are in agreement with the available experimental and other theoretical data. (C) 2010 Elsevier B.V. All rights reserved.