The edge function method for anisotropic elasticity is based on the complex variable formulation and on the superposition of analytical solutions to the field equations. Herein the method is used in the study of anisotropic materials with holes and cracks. Several examples are studied in order to provide confidence in the model through literature comparisons. The effects of anisotropy and ellipticity of the cavities are examined. The potential of the method for assessing complex stress states is demonstrated through a numerical investigation of a sheet with several cracks and cavities.