Experiments of technological interest for the project of laser isotope separation of uranium (Atomic Vapor Laser Isotope Separation, 'AVLIS') have yielded experimental data concerning the hyperfine structure (hfs) of levels of atomic uranium. The present paper reports on these data, their obtention and a parametric interpretation by the Condon Racah-Slater method. The experimental setup uses a Laser Induced Fluorescence technique in an atomic beam. Nevertheless, these experiments provide data for 28 low odd levels and 22 even levels, with an accuracy that is sufficient for a theoretical interpretation. Following the interpretation of the fine structure of the lower levels of atomic uranium by Guyon, it was reasonable to undertake a parametric interpretation of the hfs data concerning 22 of these levels on the basis of the configuration 5f36d7s2.