The problem of transverse-magnetic plane-wave scattering from a rectangular channel in a perfect conducting plane is investigated. A Fourier-transform technique is employed to express the scattered field in the spectral domain in terms of parallel-plate waveguide modes. An approximate series solution for scattering is presented in a closed form that is valid for a high-frequency scattering regime. The presented formulation is computationally much more efficient than other existing numerical solutions.