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A set of two coupled integral equations based on a plane wave representation Of the fields in a simply connected and anisotropic medium has been derived in order to handle the problem of scattering by a homogeneous anisotropic cylinder for an obliquely incident plane wave of arbitrary linear polarization. The unknowns are scalar, the range of integration is finite, and the kernels are not singular. Numerical results are presented and discussed in detail. The gyrotropic type case is emphasized, and it is found that as in the isotropic case, the depolarization is the same for transverse electric (TE) and transverse magnetic (TM) incident waves.