Summary: In electrical impedance tomography, measurements of an applied electrical current and the corresponding electrical potential are made on a finite number of electrodes placed on the boundary of an object. These measurements are then used to reconstruct the electrical conductivity distribution in the interior of the object. Iterative solutions of this inverse problem involve frequent solution of the forward problem, and it is therefore important to be able to model the current flow through the electrodes. This paper discusses one such model and describes how the related boundary value problem can be solved using semi-analytical and numerical techniques. Some conclusions regarding the proportion of the boundary that should be covered by electrodes are also drawn.