The High Flux Isotope Reactor at the Oak Ridge National Laboratory provides the highest steady-state thermal neutron flux in the western world for a wide range of experiments and for isotope production. The highest available fluxes are located in a flux trap region created inside the nested fuel elements. The experimentally determined thermal and the empirically obtained epithermal flux values along the vertical axis of the peripheral target position were fit to cosine curves, with the thermal flux ranging from 1.1 x 10(15)ns(-1)cm(-2) at outer positions to 1.5 x 10(15)ns(-1)cm(-2) at the center. The corresponding epithermal flux ranged from 3.5 x 10(13) to 7.5 x 10(13)ns(-1)cm(-2), respectively. The fast neutron flux (En > or = 0.32 MeV in two positions and En > or = 1.5 MeV in two other positions) was approximately 6 x 10(14)ns(-1)cm(-2), corresponding to a fast to thermal ratio of approximately 0.4.