A new class of binary iridium hydrides (IrxHy) is investigated in the 1 atm to 125 GPa pressure range at the ab initio level, using DFT. Upon compression a number of hydrides are predicted to stabilize in the excess hydrogen environment. Static stabilization pressure is calculated to be ∼14 and ∼5 GPa at which a dihydride (Ibam, Z = 2) and a trihydride (P63mc, Z = 2) stabilize thermodynamically, respectively. In both the di- and the trihydride iridium and hydrogen atoms form short contacts in the range typical for covalent interactions. All of the reported hydrides exhibit metallic character with the notable exception of IrH3 (P63mc, Z = 2) which exhibits a non-zero band gap and a molecular character at intermediate pressures.