Abstract: An eigenvalue method was proposed to study the singular stress field at the axisymmetric interface wedge of the fiber reinforced composites. Based on the fundamental equations of the spacial axisymmetric problem of the transversely isotropic materials and the first-order approximation assumption，a discrete characteristic equation was derived by using the displacement functions with separated variables and the meshless method. The eigenvalue was related to the order of stress singularity，and the associated eigenvector was with respect to the stress angular variations. The fiber/matrix axisymmetric interface wedge model was used to verify the validity of the proposed eigenvalue method. The order of stress singularity，the associated displacement and stress angular variations obtained by this eigenvalue method are in good agreement with those by the finite element method (FEM). Based on the order of stress singularity and the associated stress angular variations determined by the eigenvalue analysis，as well as the numerical results of singular stress fields by FEM，the stress intensity coefficient was also obtained in terms of the linear extropolation. The singular stress field around the axisymmetric interface wedge can be completely determined by the developed eigenvalue method coupling with the FEM analysis.