An anisotropic bimaterial wedge under antiplane shear is investigated. The problem is formulated by using a linear transformation method. Employing complex function representations of elastic fields, a complete form of elastic fields near the apex of an anisotropic composite wedge is derived. An anisotropic composite wedge subjected to concentrated loads is also analyzed. The transformed isotropic bimaterial wedge is first solved, and the solution for the anisotropic wedge is then obtained based on the linear transformation method. Expressions of the stress intensity factor for the composite wedge are obtained. Numerical computations are carried out to obtain the order of stress singularity and the stress intensity factors for three types of wedge shapes.