Analytical solution of eddy current testing problem for the case of a planar multilayer medium is constructed in the present paper. It is assumed that the electrical conductivity and magnetic permeability of each layer are exponential functions of the vertical coordinate. The problem is solved by the method of the Hankel integral transform. The resulting system of ordinary differential equations is solved analytically using the modified Bessel functions of the first and second kind. Two particular cases are considered in detail: (a) a single-turn coil above a conducting halfspace with varying electrical conductivity and magnetic permeability and (b) a single-turn coil above a two-layer medium where the properties of the upper layer exponentially vary with depth while the properties of the lower half-space are assumed to be constant. Results of numerical calculations of the change in impedance are presented.