In the application of electromagnetic methods to the non-destructive testing of electrically conducting materials for cracks or inclusions an electric current is applied to the specimen and the presence of a flaw is indicated by the perturbations it produces in the electromagnetic field. A number of different variants of the method can be used. The presence of a flaw may be observed by measuring either electric or magnetic field perturbations and the nature of the interrogating field will be sensitive to the choice of frequency chosen for the applied current. It is well known that when alternating current is applied to conductors the current tends to be confined to a surface layer whose depth, δ, is measured by the length 1/(ωσμ)½ where σ is the conductivity, μ is the magnetic permeability and ω the angular frequency. An important dimensionless parameter in the characterisation of the field perturbations is the ratio δ/l, where l is a length typical of the flaw dimensions. The electromagnetic field is described as a thin-skin or a thick-skin field according as this ratio is small or large respectively. In practical applications there is a need to model both thin and thick-skin fields. In the examination of surface fatigue cracks in large scale structures fabricated by welding together ferrous steel members surface fatigue cracks with depths of order 1–10 mm have been interrogated with currents at 5–6 KHz at which the skin depth is of order 0·1 mm (Dover, Collins and Michael [1]).