Abstract: An eigenvalue method was proposed to study the stresssingularity behavior at the axisymmetric interface wedge of the bondeddissimilar isotropic materials. Based on the fundamental equations of thespacial axisymmetric problem and the assumption of first-orderapproximation, the discrete characteristic equation on the stresssingularity was derived by making use of the displacement functions in theform of separated variables and the technique of meshless method. Thephysical eigenvalue is associated with the order of the stress singularity,and the corresponding eigenvector is related to the displacement and stressangular variations. A dimensionless parameter δ, which was definedas the ratio between the distance from the singular point to theaxisymmetric axis and the dimension of the singularity-dominated region, wasused to characterize the dimension effects on the stress singularitybehavior. The characteristic equation of the fiber/matrix axisymmetricinterface wedge model was solved numerically, and the order of stresssingularity, the associated displacement and stress angular variations wereobtained. It was found that the parameter δ influenced both thestrength and the order of the stress singularity, and the analyticalsolutions derived by the quasi first-order approximation was just a specialcase while δ>>1.