We present the formulation of elliptical corrugated waveguides with a concentric circular hole using the fieldmatching method and the addition theorem for Mathieu functions. The dispersion equation and the mean interaction impedance of this structure are derived separately. The numerical results, which are generally based on the current approach, agree well with the results obtained by the commercial software package CST. As a slow-wave structure, this structure has potential applications in high power microwave amplifiers and possibly filtering structures.