The methods of Eshelby, Read, and Shockley [Acta Met.1, 251 (1953)] and of Stroh [Phil. Mag.3, 625 (1958)] for determining the anisotropic elastic field of a dislocation are reviewed briefly and several problems in their application are discussed. The Stroh method is extended to the dislocation displacement field. The resulting equations are applied to the⟨111⟩screw dislocation in cubic crystals.