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High pressure behavior of a 2D hybrid perovskite semiconductor, (BA)2PbBr4 (BA = benzylammonium), has been systematically studied via synchrotron powder X-ray diffraction over the range of 0-14.22 GPa. (BA)2PbBr4 shows a soft nature with a bulk modulus of 10(1) GPa and anisotropic linear compressibility with βa = 25(6), βb = 5.3(4), and βc = 15.1(8) TPa−1. Experiment-aided density functional theory calculations reveal that the structural changes of (BA)2PbBr4 under compression are attributed to the configurational alterations of BA+ organic cations and synergistic distortion of the (PbBr4)2− inorganic layer. Further extensive theoretical calculations of elastic tensors give full mapping of Young’s moduli, shear moduli, and Poisson’s ratios of (BA)2PbBr4, which confirm its anisotropic nature in elasticity. In addition, the photoluminescence of (BA)2PbBr4 exhibits a significant red-shift and an intensity decrease in response to hydrostatic stress which respectively arise from the contractions of Pb–Br bonds and distortions of PbBr6 octahedra in the inorganic layer mediated by the configurational alterations of BA+ cations upon compression.