Friction-welded dissimilar metals are widely applied in automobiles, rolling stocks, machine tools, and various engineering fields. Dissimilar metals have several advantages over homogeneous metals, including high strength, material property, fatigue endurance, impact absorption, high reliability, and vibration reduction. Due to the increased use of these metals, understanding their behavior under stress conditions is necessary, especially the analysis of stress singularity on the interface of friction-welded dissimilar metals. To establish a strength evaluation method and a fracture criterion, it is necessary to analyze stress singularity on the interface of dissimilar metals with welded flashes by friction welding under various loads and temperature conditions. In this paper, a method analyzing stress singularity for the specimens with and without flashes set in friction-welded dissimilar metals is introduced using the boundary element method. The stress singularity index (${lambda}$) and the stress singularity factor (${Gamma}$) at the interface edge are computed from the stress analysis results. The shape and flash thickness, interface length, residual stress, and load are considered in the computation. Based on these results, the variations of interface length (c) and the ratio of flash thickness ($t_2/t_1$) greatly influence the stress singularity factors at the interface edge of friction-welded dissimilar metals. The stress singularity factors will be a useful fracture parameter that considers stress singularity on the interface of dissimilar metals.