The high-pressure behavior of tetragonal SrMoO 4 was analyzed by Raman and optical-absorption measurements. Pressures up to 46.1 GPa were generated using diamond-anvil cells and Ne or N 2 as quasi-hydrostatic pressure-transmitting media. A reversible phase transition is observed at 17.7 GPa. A second transition is found at 28.8 GPa and the onset of a third one at 44.2 GPa. The pressure dependence of Raman-active modes is reported for the different phases and the pressure evolution of the fundamental band-gap reported for the low-pressure phase. The observed changes in the Raman spectra contradict the structural sequence determined from previous experiments performed under higher non-hydrostaticity. This fact suggests that deviatoric stresses can influence pressure-driven transitions in scheelite-type oxides. We also report total-energy, lattice-dynamics, and band-structure calculations. They reproduce accurately the behavior of the physical properties of the low-pressure phase and predict the occurrence of phase transitions at pressures similar to experimental transition pressures. According to theory, the high-pressure phases have monoclinic and orthorhombic structures, which are much more compact than tetragonal scheelite. Theoretical results and experiments are compared with previous studies. V C 2013 American Institute of Physics.