Useful yields from resonance ionization mass spectrometry can be extremely high compared to other mass spectrometry techniques, but uranium analysis shows strong matrix effects arising from the tendency of uranium to form strongly bound oxide molecules that do not dissociate appreciably on energetic ion bombardment. We demonstrate a useful yield of 24% for metallic uranium. Modeling the laser ionization and ion transmission processes shows that the high useful yield is attributable to a high ion fraction achieved by resonance ionization. We quantify the reduction of uranium oxide surface layers by Ar+ and Ga+ sputtering. The useful yield for uranium atoms from a uranium dioxide matrix is 0.4% and rises to 2% when the surface is in sputter equilibrium with the ion beam. The lower useful yield from the oxide is almost entirely due to uranium oxide molecules reducing the neutral atom content of the sputtered flux. We demonstrate rapid isotopic analysis of solid uranium oxide at a precision of <0.5% relative standard deviation using relatively broadband lasers to mitigate spectroscopic fractionation.