In the present study, singular stress fields in three-dimensional dissimilar material joints are investigated at a vertex and along a free edge (a singular line) of an interface. The conservative integral formulation based on Betti's reciprocal principle is extended for analyzing the intensity of singularity at a point located on the singular line of three-dimensional bi-material joints. Models of difference angles between side surfaces are used to investigate the influence of the angles on the stress singularity characteristics. Finally, relationship between the intensity of singularity at the vertex and that at a point located on the singular line is discussed.