X-ray diffraction studies have been performed on UP powder for pressures up to 51 GPa using synchrotron radiation and a diamond-anvil cell. At ambient pressure UP has the rocksalt structure. The bulk modulus has been determined to B0=102(4) GPa and its pressure derivative to B0’=4.0(8). The cubic phase has been found to transform to a new phase, UP II, at about 10 GPa. UP II can be characterized by a rhombohedral Bravais lattice. UP II transforms to an orthorhombic phase, UP III, at 28 GPa. No volume change has been observed at the two transitions. The influence of the 5f electrons on the transformations is discussed.