With the development of high quality and high efficiency of urban rail transit, the fatigue strength of engineering and mechanical equipment has attracted more and more attention. The failure of mechanical structures arises from various forms of defects, such as cracks, inclusions, holes, etc. The singularity stress is an important cause of crack initiation at material defects. The novel super singular element is based on numerical eigen-solutions of singular displacement and stress fields and the Hellinger-Reissner variational principle. It is a special element that contains the corner of a defect and can analyze the singular elastic field. Compared with other singular elements, it is versatile and has nothing to do with the size of the element. It can be connected with conventional elements without any transition elements. It can be applied to singular stress field analysis of any interface corner and any material combination. The article mainly reviews the application of the novel supe singular elements in the crack tip, inclusion corner tip, notch corner tip, hole corner tip and multiphase materialsinterface in 2D or 3D, which has a certain guiding significance on how to use this element to analyze singular stress field.