Several monouranium and diuranium polyhydride molecules were investigated using quantum chemical methods. The infrared spectra of uranium and hydrogen reaction products in condensed neon and pure hydrogen were measured and compared with previous argon matrix frequencies. The calculated molecular structures and vibrational frequencies were used to identify the species present in the matrix. Major new absorptions were observed and compared with the previous argon matrix study. Spectroscopic evidence was obtained for the novel complex, UH4(H-2)(6), which has potential interest as a metal hydride with a large number of hydrogen atoms bound to uranium. Our calculations show that the series of complexes UH4(H-2)(1,2,4,6) are stable.