This paper introduces an algorithm for coupling the boundary element method and the scaled boundary finite element method. Although the particular application concerns the determination of stress intensity factors at crack tips, the approach is general in nature. The motivation for the work is the combination of the semi-analytical solution accuracy of the SBFEM with the geometric flexibility of the BEM for general engineering usage. The paper presents the development of the algorithm along similar lines to FEM/BEM coupling approaches. Example problems verify the accuracy of the approach, even for coarse discretisations, and demonstrate excellent convergence properties of the algorithm.