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In this paper, a method of moments (MoM) implementation of surface integral equations (SIEs) is presented for uniaxial dielectric materials using closed-form dyadic Green's functions. The standard Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) SIE is adapted for homogeneous uniaxial materials. A challenge in the implementation was the evaluation of the self impedance matrix elements and singularities due to the distinguished axis of the uniaxial media. For validation, bistatic scattering patterns of uniaxial targets are computed and compared with the well-known finite-element boundary integral (FE-BI) method solutions. A parametric study of the radiation by dipoles placed within high-contrast uniaxial layers is also presented for various distinguished axis orientations.