The solution to electromagnetic scattering by inhomogeneous oblate spheroidal particles is obtained for any polarized incident wave on the theories of spheroidal wave functions and average electric fields. And calculations are made for redar backscattering cross-section of a two-layered spongy ice hailstone with an arbitrary size and condition. The nucleus of the hailstone is considered as an ice oblate spheroid and the shell is filled with a mixture of ice and liquid water.