Abstract: The basic analytical solutions of plane notch problem are used to formulate finite elements, and the proposed elements are used to analyze the plane notch structure in turn. Following the analysis to the existence intervals of the Williams equations, the subregion accelerated Müller method is used to calculate the eigenvalues of plane notch problems. From the Williams stress function, the basic analytical solutions of the stress field at the tips of V-notchs are first derived and then used as the trial functions to formulate the element: ATF-VN. Meanwhile, the Subregion mixed energy principle is used in the formulation of the stiffness matrix. In this paper, a systematic research is done to analyze the factors that influence the results, such as the element抯 size and the stress item number.