The structure, electronic, elastic and vibrational properties of the Cu2TMAl (TM=Sc, Ti, Cr) Heusler compounds have been investigated in detail by employing an ab initio pseudopotential method and a direct method within a generalized gradient approximation (GGA-PBE) of the density-functional theory (DFT) scheme. Calculated lattice parameter values are in excellent agreement with recent experiments. In the present study, Cu2ScAl and Cu2TiAl does not show any magnetic moments, whereas the Cu2CrAl has magnetic moment of 2.95 μB per formula unit. From electronic band structures we have found that these compounds have a metallic nature. The elastic constants Cij are computed using the total energy variation versus strain technique. The calculated elastic constants and bulk modulus are reported and compared with earlier available theoretical calculations. Phonon frequency for Cu2TMAl (TM=Sc, Ti, Cr) Heusler compounds have been computed and plotted along with high symmetry directions.