A resonance self-indication technique, that measures nondestructively the thickness of fissile materials, has been investigated. This method utilizes the resonance structure in the neutron fission cross section by passing an epithermal beam of neutrons through the sample and then to thin fission detectors that are sensitive to the resonance absorption lines in the transmitted flux corresponding to the resonance reaction peaks. The measurements included samples of 283U, 235U, and 239Pu with thicknesses ranging from 5 to 270 mils. The present measurements indicate that this technique could be used to measure the thickness of 239Pu with an accuracy of 1 to 3%, and an accuracy of 2 to 10% for 233U and 235U for thicknesses <150 mils. The influence of extraneous material in the samples was greatly reduced by using ratios of different fission detectors in the measurement. Computer calculations of the fission rates were made, and the theoretical results are in good agreement with the measurements.