High-pressure X-ray diffraction of PdH x and PdD x demonstrates that these materials remain in a face-centered cubic (fcc, Fm3̅m) structure to megabar pressures at room temperature. The volumes indicate stoichiometric compositions under pressure with x = 1 for both materials. No indication of any phase transition was observed up to the highest pressures reached in the experiments. A third-order Birch–Murnaghan equation of state used to fit the pressure–volume data gives V 0 = 10.73 (±0.03) cm3/mol, K 0 = 147 (±11) GPa, and K 0′ = 4.7 (±0.5), whereas a Vinet fit gives V 0 = 10.74 (±0.03) cm3/mol, K 0 = 143 (±11) GPa, and K 0′ = 5.1 (±0.5), for the combined data for both PdH x and PdD x . The results are used to obtain the pressure dependence of the effective volume of H and D atoms in PdH x and PdD x to megabar pressures for comparison with other simple hydrides with implications for superconductivity in this class of materials.