The scaled boundary FEM (SBFEM) is a novel semi-analytical approach, which combines the advantages of the FEM and BEM with appealing features of its own. In this paper, the method is applied to analyse the quadruple corner-cut ridged elliptical waveguide. A quarter of the waveguide is adopted and divided into a few subdomains. SBFEM only discretizes the surface boundaries of the subdomains in the sense of FEM, and no discretization of side-face boundaries is needed, leading to great flexibility in mesh generation with very few nodes. It transforms the governing PDEs to ODEs of the radial parameter by the variational principle. The radial differential equation is then solved fully analytically without adoption of any numerical scheme, which brings out the inherent advantage for solving a singularity problem. Based on the SBFEM governing equation and introducing the dynamic stiffness of waveguide, a generalised eigenvalue equation with respect to cut-off wave number is formulated by a continued fraction solution without introducing an internal mesh. The numerical example demonstrates the simplicity, excellent computation accuracy and efficiency of the present SBFEM approach. Influences of corner-cut ridge dimensions on the cut-off wave numbers of modes are examined in detail. Therefore, these results provide an extension to the existing design data for ridged waveguides and are considered helpful in practical applications. Copyright © 2011 John Wiley & Sons, Ltd.