An analytical solution to the problem of two-dimensional scattering by a homogeneous anisotropic elliptic cylinder is derived. With the aid of an integral equation based on a plane wave representation of the field and the series expansions in terms of Mathieu functions

the transmitted fields of the elliptic cylinder and radar cross sections per unit length under a transverse-electric illumination are obtained. Some numerical results are presented

the effect of electric size and material of elliptic cylinders on the radar cross sections is discussed. The data are in agreement with those available as expected when the elliptic cylinder degenerates to a homogeneous anisotropic circular one.