Abstract: In this paper a non-conforming finite elementeigen-analysis method based on displacement is developed to study thesingular stress and displacement fields surrounding a wedge tip. The formula is different from the existing finite elementeigen-analysis methods for asymptotic fields near the crack tip. The element is non-conforming one, and the singular transformationtechnique is not used in the assumption of displacement fields surroundingthe wedge tip. This paper presents some illustrative evaluating examples ofasymptotic singular fields surrounding arbitrary wedges and junctiontips. All calculations show that the present method needs fewer elements, yieldsmore accurate results, and can be applied more extensively.