First principles density functional theory calculations were performed to study structural, electronic, elastic, optical and vibrational properties of CoAL(2)O(4) and MnAl2O4 aluminate spinels. Computed ground state properties such as unit-cell parameter and oxygen positional parameter differ by less than 1% from previously available theoretical and experimental results. However, the bulk modulus differs by less than 4% difference from available theoretical and experimental values for CoAl2O4 and less than 10% for MnAl2O4. Zone-center phonon frequencies and the phonon spectrum along high symmetry direction together with the phonon density of states were calculated using supercell method. Bandgaps of CoAl2O4 and MnAl2O4 were obtained as 1.78 and 2.21 eV respectively. CoAl2O4 was found to be more ionic than the MnAl2O4 spinel. And quasi harmonic method was used to calculate the Debye temperature for the studied compounds.