We report a series of powder X-ray diffraction experiments performed on the soft porous crystals MIL-53(Al) and NH₂-MIL-53(Al) in a diamond anvil cell under different pressurization media. Systematic refinements of the obtained powder patterns demonstrate that these materials expand along a specific direction while undergoing total volume reduction under an increasing hydrostatic pressure. The results confirm for the first time the negative linear compressibility behaviour of this family of materials, recently predicted from quantum chemical calculations.