Using the Pulsed-Sphere Method, the leakage spectra from hollow Be spheres of 4.5, 13.8 and 19.9 cm thickness have been measured. The predicted copious production of epithermal and thermal neutrons from the 13.8 and 19.9 cm spherical shells has been verified. A quantitative comparison of measured and calculated time-of-arrival count spectra over the energy range from thermal to ∼ 15 MeV indicates that the ENDL-84 library overestimates the leakage spectra between 2 and 10 MeV and in the epithermal and thermal energy regions. In the remaining regions, the leakage spectra are underestimated. Because of the above compensation the inferred leakage multiplication for the 19.9 cm Be is ∼ 3% higher than calculations. In the case of the 13.8 cm Be, the compensation is less exact and the inferred leakage multiplication is ∼ 9% higher than calculations.