The edge function method, which involves the use of analytic solutions to model field behavior in the various parts of an elastic region, is applied to the analysis of a finite anisotropic plate with a single crack. Analytical solutions for the stress singularities at each crack tip facilitate the inexpensive calculation of accurate values of the stress intensity factors. A boundary Galerkin variational principle is used to match the boundary conditions. The method is applicable to isotropic and anisotropic materials and is demonstrated for a number of fracture problems involving variation of the crack position, crack orientation and material orientation. For the range of geometries examined in this paper, the calculated values of the stress intensity factors do not show a major dependence on the material anisotropy. The formulation of the method makes it easily applicable to the study of the interaction of several cracks and also to a limited study of crack propagation or damage development in a composite laminate.