A new technique for element specific imaging in computerised tomography has been developed. The technique allows two or more elements to be imaged independently of the matrix in which they are contained. The technique uses a filtered tube source of x-rays and low energy resolution detector. Fractional transmittance measurements were recorded at a number of tube potentials along each of the beam paths required for standard CT reconstruction. This data was used to obtain monochromatic information about the absorber. K-edge differential absorptiometry was then used to obtain the equivalent thickness of each element of interest. Using the algebraic reconstruction technique (ART), element specific images were generated. The technique was successfully used to separately image iodine and barium distributed in a water matrix. In a refinement of the technique, a single channel analyser was used to increase the percentage of counts in the fractional transmittance measurement providing information about the elements of interest. Using this approach, cadmium and indium, elements with a K-edge separation of 1.23keV, were separately imaged. The technique was also tested for matrix independence and linearity using homogeneous samples. Using computer simulations the optimum operating conditions and characteristics of the technique were examined. Finally, future developments of the technique are discussed along with a possible application.