Electrical impedance tomography (EIT) is a technique in which images representing the cross-sectional distribution of electrical impedance within a threedimensional object are reconstructed from measurements on the object surface. In this work, some developments of image reconstruction algorithms aimed at increasing the value of this technique in the field of medical diagnosis are studied. The electrical properties of biological tissue and the possibilities for medical applications of EIT are first reviewed. The physical and mathematical basis for EIT is then. examined with particular regard for the assumptions required. Following a review of published work on image reconstruction methods, a set of specifications thought useful to advance the utility of EIT as a clinical imaging modality is proposed, together with an approach to image reconstruction designed to fulfil these specifications. A series of computer simulations of the image reconstruction problem is then used to investigate the performance of this reconstruction approach on simple, known, impedance distributions, and to develop the method to the stage of a complete reconstruction algorithm. The algorithm is then tested on a series of data sets produced by measurements on a physical phantom, and on a set of measurements made on a volunteer human subject.