We determine the elastic constants and the Raman spectra of spinel under pressure using density functional perturbation theory. Like other spinels, MgAl 2 O 4 shows an increasing bulk modulus and a weakly varying shear modulus under pressure. The Raman spectrum is dominated by two mains peaks whose intensities decrease under pressure. The theoretical Raman spectra of disordered spinel shows a better agreement with measurements on natural samples than the ordered one. We also investigate the high-pressure stability of different structures and find the calcium titanate type to be the stable phase beyond 45GPa.