We investigate the electronic, elastic and thermodynamic properties of nanolaminate Cr2MC(M=Al, Ga) by using the ab initio pseudopotential total energy method. Our results show that they have shown almost identical volume compressibilities. The axial compressibility investigations show that the c axis is always stiffer than a axis. The internal coordinate calculations revealed that the values of Cr atoms in Cr2AlC are always larger than those in Cr2GaC. The elastic constants calculations demonstrated the structural stability within 050 GPa. The obtained bulk moduli by quasi-harmonic Debye model observed that the bulk moduli of Cr2MC(M=Al, Ga)decrease with temperature at 0 GPa, but increase at 300 GPa. We also found that the Debye temperatures of Cr2GaC are always smaller than those of Cr2AlC at any conditions. However, the opposite cases can be found in thermal expansion coefficients, Grneisen parameter, entropy and heat capacity when comparing their respective counterparts between Cr2GaC and Cr2AlC. The electronic density of states and energy band distribution demonstrated that the Cr2MC(M=Al, Ga) have shown similar profiles with the only exception of the more localized s and p electrons in Cr2GaC than their respective counterparts in Cr2AlC.