An analysis of eddy-current induction is presented for applications in low-frequency electromagnetic nondestructive evaluation (NDE) using superconducting quantum interference devices (SQUID's). Analytical expressions are developed for the induced eddy currents, as well as the resulting magnetic fields produced by circular excitation coil above conducting plates of infinite and finite thicknesses. The in-phase (0°) and quadrature-phase (90°) components of the eddy-current density are plotted for the low-frequency excitations characteristic of SQUID NDE. The quadrature-phase eddy current has a peak value at the surface of conducting plates, while the in-phase eddy current is maximal at a characteristic depth in the conducting material. Also, both the quadrature- and in-phase eddy currents change signs at characteristic depths that depend on the skin depth. These features can be exploited in determining the depth of material defects. The expression for the magnetic field produced by an excitation coil above a conducting plate of finite thickness is then used to estimate the SQUID's response due to corrosion or variation in material thickness. The expressions derived here can be used to model the magnetic signature of localized defects.