Here we report on the first structural and optical high-pressure investigation of MASnBr3 (MA = [CH3NH3]+) and CsSnBr3 halide perovskites. A massive red shift of 0.4 eV for MASnBr3 and 0.2 eV for CsSnBr3 is observed within 1.3 to 1.5 GPa from absorption spectroscopy, followed by a huge blue shift of 0.3 and 0.5 eV, respectively. Synchrotron powder diffraction allowed us to correlate the upturn in the optical properties trend (onset of blue shift) with structural phase transitions from cubic to orthorhombic in MASnBr3 and from tetragonal to monoclinic for CsSnBr3. Density functional theory calculations indicate a different underlying mechanism affecting the band gap evolution with pressure, a key role of metal-halide bond lengths for CsSnBr3 and cation orientation for MASnBr3, thus showing the impact of a different A-cation on the pressure response. Finally, the investigated phases, differently from the analogous Pb-based counterparts, are robust against amorphization showing defined diffraction up to the maximum pressure used in the experiments. Copyright © 2019 American Chemical Society.