Based on the asymptotic fields near the singular points in two-dimensional isotropic and orthotropic elastic materials, the eigenequation as well as the displacement and singular stress fields near the interface edge, with an arbitrary wedge angle for the orthotropic material, in orthotropic/isotropic bi-materials are formulated explicitly. The advantages of the developed approach are that not only the eigenequation is directly given in a simple form, but also the eigenvector is no longer needed for the determination of the asymptotic fields near the interface edge. This approach differs from the known methods where the eigenequation is constantly expressed in terms of a determinant of matrix, and the eigenvector is required for the determination of the asymptotic fields. Therefore, the solution proposed in this paper is more convenient and effective for the analysis of the singular stresses near the interface edge in the orthotropic/isotropic bi-material. To demonstrate the validity of the presented formulae, an example is selected for the comparison of analytical and FEM results. According to the theoretical analyses, the influences of the wedge angle and material constant of the orthotropic material on the singular stresses near the interface edge are discovered clearly. The results obtained may give some references to certain engineering designs such as the structural repair or strengthening.