Abstract: The shape optimization of a rigid inclusion in an elastic plane under concentrated loads is considered. The conformal mapping technique and extended Schwarz principle integrated with the analysis of singularity of complex stress functions are adopted. A number of examples of the rigid inclusion with different shapes, such as elliptical, triangular and square inclusion, to account for a wide range of shape variations are discussed. Numerical results and graphs are presented, showing that the maximum interface stresses vary with the shape of inclusion. The shape resulting in minimum interface principal stress is obtained. Some suggestions are made in regard to the design of the shape of rigid inclusion.