The structural, elastic, electronic and phonon properties of Cu2MnZ (Z=Al, Si, Ge, Ga, Sn, Sb, In) are investigated by first-principles calculations based on density functional theory. In this approach the local-density approximation (LDA) and generalized gradient approximation (GGA) are used for the exchange-correlation (XC) potential. The calculated lattice constant, bulk modulus, and elastic constants are in agreement with the previous ab-initio calculations and available experimental results. Electronic properties are discussed from the calculations of band structure and density of states. The direct method is used to derive the phonon frequencies and density of states.