Electrical impedance tomography (EIT) may be used to image brain function, but an important consideration is the effect of the highly resistive skull and other extracerebral layers on the flow of injected current. We describe a new reconstruction algorithm, based on a forward solution which models the head as four concentric, spherical shells, with conductivities of the brain, cerebrospinal fluid, skull and scalp. The model predicted that the mean current travelling in the brain in the diametric plane for current injection from polar electrodes was 5.6 times less than if the head was modelled as a homogeneous sphere; this suggests that an algorithm based on this should be more accurate than one based on a homogeneous sphere model. In images reconstructed from computer-simulated data or data from a realistic saline-filled tank containing a real skull, a Perspex rod was localized to within 17% or 20% of the tank diameter of its true position, respectively. Contrary to expectation, the tank images were less accurate than those obtained with a reconstruction algorithm based on a homogeneous sphere. It is not yet clear if the theoretical advantages of this algorithm will yield practical advantages for head EIT imaging; it may be necessary to proceed to more complex algorithms based on numerical models which incorporate realistic head geometry. If so, this analytical forward model and algorithm may be used to validate numerical solutions.