Electrical resistance tomography permits the determination of the spatial distribution of electrical resistivity by non-destructive means. The technique may be applied to the study of flow through porous media by following the changes in resistivity distribution within a soil or rock core as an electrolytic tracer is passed through the specimen. Image reconstruction of the electrical resistance tomography data may be achieved by robust regularized nonlinear inverse methods provided data errors are suitably characterized. The procedure is reported here for a natural (undisturbed) soil core using four planes of 16 electrodes placed around the boundary of the core. The experiment was performed with a dye tracer that provided, by destructive slicing, visual verification of the flow pathways observed with the tomographic imaging.