The general problem of two semi-infinite elastic media with different properties bonded to each other along a plane and containing a series of concentric ring-shaped flat cavities is considered. Using the Green’s functions for the semi-infinite plane, the problem is formulated as a system of simultaneous singular integral equations. Closed-form solution of the corresponding dominant system with Cauchy kernels is given. To obtain the complete solution, a technique reducing the problem to solving a system of linear algebraic equations rather than a pair of Fredholm integral equations is outlined. The examples for which the contact stresses are plotted include the bonded media with an axially symmetric external notch subject to axial load or homogeneous temperature changes and the case of penny-shaped crack.