[en] The electronic structure, dielectric function, Debye temperature and elastic properties of Ti₂AlN and Cr₂AlC were studied by means of pseudo-potential plane-waves method using the density function theory. The exchange-correlation approximation energy was determined by generalized gradient approximation method. The experimental lattice constants and the internal parameters were used in the calculation. The dielectric function was calculated by energy band theory, and the elastic constants were obtained using the static finite strain technique. The bulk and shear module, Young's module and Poisson's ratio for ideal polycrystalline Ti₂AlN and Cr₂AlC aggregates were derived in this paper. The Debye temperature of Ti₂AlN and Cr₂AlC from the average sound velocity was also estimated. The obtained results are in agreement with the available theoretical data.