Abstract: The V-notch analysis of orthotropic materials requires the eigenvalues of a problem. Firstly, the material characteristic matrixes of the orthotropic materials and the boundary characteristic equations based on the boundary conditions are derived. Then simplified Stroh formula for orthotropic materials is given. Finally, the eigenvalues of symmetric and antisymmetric plane problems of different materials are studied using the sub-region accelerated Müller method. With the introduction of the boundary-withdraw and split-factor methods, the sub-region accelerated Müller method shows the advantages of fast convergence, high precision and easy to implement. It is also an effective method to avoid the calculation of the previous roots. Thusly, the convergence speed can be increased.