The problem of determining stress distributions induced by holes has aroused considerable interests for almost half a century. Of various holes the elliptic shape and its geometric limits such as circles and cracks have evoked the most interest among researchers. If the stress concentration is of more concern, the optimization in a class of hole shapes has shown that the optimized hole is not necessarily the elliptic type. However, due to the requirement of one-to-one mapping, most of the solutions found in the literature either by Lekhnitskii or Stroh formalism are valid only for the elliptical holes. Exact analytical solutions have been found for various shapes of holes if the materials are restricted to the isotropic ones (Savin, 1961).