Cubic (space group: Fmm) iridium phosphide, Ir2P, has been synthesized at high pressure and high temperature. Angle-dispersive synchrotron X-ray diffraction measurements on Ir2P powder using a diamond-anvil cell at room temperature and high pressures (up to 40.6 GPa) yielded a bulk modulus of B0 = 306(6) GPa and its pressure derivative B0' = 6.4(5). Such a high bulk modulus attributed to the short and strongly covalent Ir-P bonds as revealed by first - principles calculations and three-dimensionally distributed [IrP4] tetrahedron network. Indentation testing on a well-sintered polycrystalline sample yielded the hardness of 11.8(4) GPa. Relatively low shear modulus of ~64 GPa from theoretical calculations suggests a complicated overall bonding in Ir2P with metallic, ionic, and covalent characteristics. In addition, a spin glass behavior is indicated by magnetic susceptibility measurements.