In this paper, we analyze theoritically the propagation and radiation characteristics for elliptical corrugated waveguides. The solutions of wave equations in an elliptic cylinder system are obtained in terms of Mathieu functions of 1st and 2nd kind. The electromagnetic fields in the elliptical corrugated waveguide can be represented by series and products of angular and radial Mathieu functions. By using impedence matching at the boundary between the inner region and the slot region, characteristic equations are derived. Then the characteristic equation is solved for $HE_{11}$ mode which is dominant mode in the elliptical corrugated waveguide and the fields in the aperture is calculated. And the propagation pattern for the elliptical corrugated waveguides is calculated through the field equivalence principle