Eddy-current induction by a coaxial circular air-cored coil in a cracked borehole is considered in the limit of small electromagnetic skin depth. A closed form expression is derived for the change in coil impedance ΔZ due to a long axial crack with constant depth and opening based on an extension of the Lewis extended surface impedance boundary conditions to a cylindrical geometry. The theoretical predictions are compared with experimental measurement of ΔZ for a series of boreholes containing wire-cut slots in 2024 Al alloy test specimens. The model predictions were in good agreement with experiment for smaller slot depths, with the accuracy tending to decrease as the slot depth increased. In all cases, the predictions were superior to those based on a simple Born approximation.