In this paper, the singular stress in a wedge-shaped region composed of two materials is studied as a plane problem. An expression is presented for the singular stress field in the vicinity of the corner. When the eigenvalue λ, the root of the eigenequation, is a complex number, the intensity of the singular stress field is defined in terms of two real constants. When A is a real number, the intensity of the singular stress field is defined in terms of one real constant. Based on the numerical results for several special wedges, the mode of singular stress distribution is studied in detail.