Calculations have been performed to study the structural, electronic, elastic, mechanical, thermodynamical and phonon properties of LuS and LuTe with the generalized gradient approximation for exchange and correlation. The calculated lattice constants, bulk modulus, its pressure derivative and elastic constants are calculated. The calculated values of lattice constant are in good agreement with the experimental and theoretical results. The elastic constants have been derived from the slopes of the acouistic branches in the phonon dispersion-curves. The electronic band structure and, total and partial density of states of these compounds have been computed and analysed. The phonon dispersions curves of LuSe and LuTe for B2 phase are computed using density functional perturbation theory (DFPT) with generalized gradient (GGA) approximations. We also used the quasiharmonic approximation to calculate some thermodynamic properties such as constant-volume specific heat capacity of the B2 phase of LuS and LuTe compounds.