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The method of modal expansions is a fundamental technique for solving the electromagnetic boundary value problems. As its practical alogrithm, the point-matching method has been used but frequently failed. A new computer-aided procedure based on the method of modal expansions is presented and applied to the scattering from a periodic structure composed of a perfectly conducting surface. As an example, the scattering from the grating with a sinusoidal height profile is calculated. It is demonstrated numerically that the new procedure leads to desirable results, while the point-matching method does not. Several physical characteristics on the reflection grating including the diffraction anomalies are explored.