The solutions to the problems of two-dimensional anisotropic elastic solids containing elliptical holes or polygon-like holes have been presented in Hwu (Anisotropic elastic plates. Springer, New York, 2010) for various kinds of loading conditions. Exact closed-form solutions are obtained for the elliptical holes, which are also applicable for the circular holes and cracks. Whereas the solutions to the polygon-like holes are generally approximate. The ellipse, triangle, oval, square, pentagon, and so on are all included as special cases of polygon-like holes. Most of the solutions presented in this chapter are expressed in terms of the variables mapped from an ellipse or a polygon to a unit circle. Since the transformation is in general not one-to-one, special attention shall be made on the proper selection of the mapped variables. With this concern, some remarks are added in the related sections to assist the presentation of the associated computer codes. Section 6.1 covers the problems of elliptical holes under uniform load, in-plane bending, arbitrary load along the hole boundary, point force and dislocation. Section 6.2 includes the problems of polygon-like holes under uniform load and in-plane bending. Functions for common use and examples for hole problems are then presented in the last two sections.