In this paper, a new way was proposed to evaluate the orders of singularity for plane V-notch problems. Based on an asymptotic displacement field in terms of radial coordinates at the V-notch tip, the governing equations of the elastic theory were transformed into an eigenvalue problem of ordinary differential equations (ODEs). Then the interpolating matrix method which was a numerical method of solving two-point boundary valve problems was further developed to solve the general ODEs eigenvalue problem. Thus the singularity orders of the V-notch problem are determined through solving the corresponding ODEs by means of the interpolating matrix method. In addition, the associated eigenvectors of the displacement and stress fields near the V-notches are also obtained.