The V-notch asymptotic displacement field was derived through an approach based on the Williams’ series expansion and linear algebraic transforms. By incorporating the displacement expressions to the common isoparametric elements, the enriched and transition element displacement model were obtained, and then the enriched finite element equation was derived consequently. The enriched finite element model for a V-notched bi-material three-point bending beam and an orthogonal bonded materials interface end plane problem were constructed. The stress intensity factors can be solved directly from the finite element equation. Comparisons between the results and the published data computed with other algorithm indicate that the present method is correct and can be used to analyze the fracture property of the Vnotched bimaterial structure.