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The scattering of a two‐dimensional Gaussian beam wave by a perfectly conducting or dielectric cylinder centered off both the beam axis and the beam waist is treated by the Fourier‐series‐expansion method. The incident‐beam fields are expanded in a Fourier series with respect to the polar angle in a cylindrical coordinate, and the expansion coefficients are numerically evaluated. Several scattering patterns are obtained by the use of these expansion coefficients, and the dependence of the scattering characteristics on the offset of the incident‐beam wave is examined.