A method and apparatus for non-invasively determining the internal composition of objects are disclosed. The object of interest is probed with low energy, monoenergetic narrow beams of fast neutrons. The object is generally placed on a conveyor belt which is positioned between the accelerator and the detectors. Detectors, positioned at radial angles corresponding to the resonance energy levels of certain preselected elements, measure the neutrons that are not absorbed or scattered by the elements in the object and thus pass straight through the object. The information obtained from the detectors can then be used for subsequent tomographic reconstruction.