The radiation from a plane waveguide with an infinite anisotropic impedance flange into the homogeneous isotropic magnetodielectric is rigorously studied by using the multimode approximation. The fields in the waveguide are expanded into series of the waveguide modes and in the half-space - as discontinuous integrals on the plane wave. Continuity of the tangential aperture fields and vector boundary conditions for anisotropic impedance flange yields integral equations for considered problem.

Numerical results for the polar pattern, reflection coefficient of the basic mode and reflection coefficients of high-orders modes are presented.