The volume compression of BaNd2CuO5 (brown phase) and BaLu2CuO5 (green phase) have been measured to 8.67 and 9.23 GPa, respectively, utilizing a diamond anvil high-pressure cell and energy dispersive X-ray powder diffraction. The pressure dependence of the volume of the orthorhombic BaLu2CuO5 and tetragonal BaNd2CuO5 unit cell, as determined by a least-squares fit of the data, are both linear and follow the equations of V=−1.615P+260.62 Å3, and V=−1.9001P+476.92 Å3, respectively. While linear compressions of the unit cell parameters of BaNd2CuO5 exhibit isotropic compressive behavior within our experimental error, BaLu2CuO5 shows somewhat anisotropic compressibility behavior. From the observed data, the bulk modulus of BaNd2CuO5 is determined to be 161±8 GPa and the Young's modulus is estimated to be 193 ±9 GPa. For BaLu2CuO5, the corresponding bulk modulus and the Young's modulus are estimated to be 251±13 GPa and 301±16 GPa, which are significantly greater than those of the brown phase and the high-Tc superconductor Ba2YCu3O6+x. No evidence of a pressure-induced phase transformation was found in either compound in the pressure range studied.