Conventional computerized axial tomography images show the spatial variation in the linear attenuation coefficient in a cross-section of a specimen. However, no information is present to enable one to predict the location nor concentration of an atomic element in the image. Differential X-ray absorptiometry is a well established analytic technique for determining the concentration of an atomic element in a specimen. In this thesis, it is shown that by applying differential X-ray absorptiometry to computerized axial tomography, element specific images of a cross-section of a specimen can be produced using either radioisotope or tube sources. Differential X-ray absorptiometry involves the measurement of incident and transmitted photon fluxes, in narrow energy bands which straddle an absorption edge of the atomic element of interest, for a collimated beam through a specimen. At an absorption edge there is a sudden jump in the element’s attenuation coefficient. It is this phenomenon that is the basis of differential X-ray absorptiometry. From the measured photon counts, the equivalent thickness (kg/m2) of an element along a path length can be determined. Two technique are developed here. The first is for the case when radioisotopes are used. It involves two measurements, i.e. with and without the element of interest present. The second is for the case when an X-ray tube source is used. In this case, the equivalent thickness is found by extrapolation of the count data to the absorption edge of the absorption edge. Using this technique, several elements can be imaged simultaneously. By measuring the equivalent thickness at many different orientations to the specimen, enough data can be collected so that an image of the cross-section, showing elemental concentration, can be produced. Special mathematial algorithms, called reconstruction algorithms are required.The computer programs written to generate reconstructed images are outlined. The sensitivities of the techniques developed for imaging atomic elements are studied both experimentally and theoretically. Equations are derived herein to calculate the minimum concentration of an element that can be imaged in a specimen. Using these equations, the most sensitive X-ray energy to an element in a chosen specimen can be determined. In addition, some example calculations are given and these are compared with experimentally obtained values to verify the equations. Finally, descriptions of the experimental apparatus setup and the experiments undertaken are given. The elements which are imaged include palladium, silver, cadmium, indium and caesium. In all cases the concentrations are of the order of several kilogrammes per cubic metre. Finally, possible future developments are considered.