SUMMARYScattering of a TM plane wave from a finite periodic surface is studied by the spectral formalism. First, the diffraction beam, the optical theorem, the total scattering cross section and the relative power of diffraction beam are defined. By use of the principle of reflection, it is shown that the spectrum of the scattered wave can be written by the boundary value only on the corrugated part of the surface. Expanding such boundary value into a Fourier series, the integral equation determining the boundary value is transformed into a matrix equation of the Fourier coefficients, which is solved numerically. Then the total power of scattering and the relative power of diffraction beam are calculated against the angle of incidence. Wood's anomaly, the beam width of a diffraction beam, and the singularity of the spectrum of the scattered wave are discussed.