The purpose of this study to derive a theoretical solutions for two elliptical inclusions that are perfectly bonded to an elastic medium (matrix) of infinite extent under antiplane loading. These two ellipses have different shear moduli, long-axial radii, short-axial radii, inclining angles, and central points. The matrix is assumed to be subjected to arbitrary antiplane loading by, for example, uniform shear stresses, as well as to a concentrated force and screw dislocation at an arbitrary point. The solutions are obtained through iterations of the Möbius transformation as a series with an explicit general term involving the complex potential functions of the corresponding homogeneous problem. This procedure is referred to as heterogenization. Using these solutions, several numerical examples are presented graphically.