X-ray diffraction experiments under high pressure have been carried out on BaFCl, BaFBr, and BaFI that belong to the family of layered ionic crystals with the matlockite PbFCl structure. Experiments up to 30 GPa with different pressure transmitting media and different powder proportions were undertaken to determine the anisotropic stress component contribution. The bulk and linear moduli were determined for each compound and structural phase transitions have been observed near 21 and 27 GPa for BaFCl and BaFBr, respectively. The difference in bond strength due to the layered properties of these compounds results in clear differences in compressibilities along the two principal directions, perpendicular and parallel to the C4 axis of the tetragonal matlockite structure. The anisotropic behavior of the unit-cell parameters observed under compression is attributed to the anisotropic coordination of the highly polarizable halogen anion. This phenomenon created a large static dipole at the halogen and involves an energy contribution that seems to stabilize the layered structure. [S0163-1829(99)03206-3]