In the present paper, we derive a solution for two circular holes or rigid inclusions that are perfectly bonded to an elastic medium (matrix) of infinite extent under in-plane deformation. These two holes or rigid inclusions have different radii and different central points. The matrix is subjected to arbitrary loading, for example, by uniform stresses, as well as a concentrated force at an arbitrary point. The solution is obtained through iterations of the Möbius transformation as a series with an explicit general term involving the complex potential of the corresponding homogeneous problem. This procedure is referred to as heterogenization. Using these solutions, several numerical examples are presented graphically.