The possibility of identifying vibrating components, in a nuclear reactor core, through the use of statistical techniques has been investigated. Mechanical vibrations produce neutron noise which appears as fluctuations in detector signals. Theory pertaining to the production of neutron noise is discussed. Vibrations are characterized by location and vibration trajectory parameters. Maximum-likelihood and confidence-region techniques were developed to estimate these parameters. Computer experiments were carried out using simulated detector signals for a simplified reactor model. The sensitivity of the techniques was investigated by parametrically studying the effects of noise level in the detector signal and the presence of external noise or bias in the model. The use of the Fisher information matrix, as a tool, to estimate the optimum number and pattern of detectors required in the identification process, was demonstrated. An experiment was performed utilizing the Iowa State University UTR-10 reactor to demonstrate the validity of the statistical techniques developed. A vibrating absorber, moving in one dimension, was operated in the fuel region and measurements were taken with four detectors. Detector responses, in terms of auto-power spectral densities, were calculated using a modified version of the computer code, Exterminator-2. The detectors were grouped into different patterns and the localization was carried out using the measured data. The vibrating absorber was located by those patterns that were selected as 'good' patterns by the information matrix analysis. The amplitude parameter was estimated within 5% of the true value;In this study, only the case of a single vibrating rod moving in a two-dimensional periodic fashion was addressed. The methods developed may be easily extended to multiple vibrations and stochastic vibrations.