The structural, electronic, elastic and thermodynamic properties of oxo- and thio-spinels have been predicted based on the ultrasoft pseudo-potential scheme as implemented in the CASTEP code. The exchange-correlation potential was treated within the generalized gradient approximation (GGA-PBE). The calculated structural parameters such as lattice constants and internal parameters are in good agreement with the available experimental data. The ground state electronic band structure revealed that CuAl2X4 (X = O, S) spinels are direct band gap semiconductors with a transition along Gamma-Gamma symmetry points. The calculated values of elastic constants satisfy the Born criteria at ambient conditions and confirm that the spinel structures of CuAl2O4 and CuAl2S4 are mechanically stable. The thiospinel structure may have a phase transition under pressure, due to the negative value of C-44. The influence of temperature and pressure on macroscopic characteristics of CuAl2O4 and CuAl2S4 compounds was estimated using the quasi-harmonic Debye model.