Abstract: A new strategy for formulating the fundamental analytical solutions by solving the characteristic equations of plane problems with anisotropic materials was proposed in this paper. And as a result, a series of independent and complete fundamental analytical solutions were successfully formulated. Firstly, the general characteristic solutions of the plane problem with anisotropic materials were obtained by calculating the determinant of the characteristic equations of the differential operator matrix. Then, the fundamental analytical solutions were formulated by substituting these general characteristics solutions into the adjoint matrix of the differential operator matrix. Finally, according to the argumentation for the independence of the fundamental analytical solutions, the series of the independent and complete fundamental analytical solutions could be simply given. The proposed strategy is quite simple and effective. And the resulting analytical solutions can be used for developing many numerical high-performance methods.